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Journal articles on the topic 'Non-compact problems'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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1

Ellis, John, K. Enqvist, and D. V. Nanopoulos. "Non-compact supergravity solves problems." Physics Letters B 151, no. 5-6 (1985): 357–62. http://dx.doi.org/10.1016/0370-2693(85)91654-5.

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2

Cavalier, L. "Inverse problems with non-compact operators." Journal of Statistical Planning and Inference 136, no. 2 (2006): 390–400. http://dx.doi.org/10.1016/j.jspi.2004.06.063.

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3

Hofmann, Bernd, and G. Fleischer. "Stability Rates for Linear Ill-Posed Problems with Compact and Non-Compact Operators." Zeitschrift für Analysis und ihre Anwendungen 18, no. 2 (1999): 267–86. http://dx.doi.org/10.4171/zaa/881.

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4

Gajic, Ljiljana. "On some optimization problems in not necessarily locally convex space." Yugoslav Journal of Operations Research 18, no. 2 (2008): 167–72. http://dx.doi.org/10.2298/yjor0802167g.

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In this note, by using O. Hadzic's generalization of a fixed point theorem of Himmelberg, we prove a non - cooperative equilibrium existence theorem in non - compact settings and a generalization of an existence theorem for non - compact infinite optimization problems, all in not necessarily locally convex spaces.

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5

O'Regan, Donal. "Boundary value problems on noncompact intervals." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 4 (1995): 777–99. http://dx.doi.org/10.1017/s0308210500030341.

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6

Damag, Faten H., Amin Saif та Adem Kiliçman. "φ−Hilfer Fractional Cauchy Problems with Almost Sectorial and Lie Bracket Operators in Banach Algebras". Fractal and Fractional 8, № 12 (2024): 741. https://doi.org/10.3390/fractalfract8120741.

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In the theory of Banach algebras, we use the Schauder fixed-point theorem to obtain some results that concern the existence property for mild solutions of fractional Cauchy problems that involve the Lie bracket operator, the almost sectorial operator, and the φ−Hilfer derivative operator. For any Banach algebra and in two types of non-compact associated semigroups and compact associated semigroups, we prove some properties of the existence of these mild solutions using the Hausdorff measure of a non-compact associated semigroup in the collection of bounded sets. That is, we obtain the existenc

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7

Aussel, Didier, and Asrifa Sultana. "Quasi-variational inequality problems with non-compact valued constraint maps." Journal of Mathematical Analysis and Applications 456, no. 2 (2017): 1482–94. http://dx.doi.org/10.1016/j.jmaa.2017.06.034.

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8

Wang, Xiangsheng. "Elliptic boundary value problem on non-compact G-manifolds." International Journal of Mathematics 28, no. 04 (2017): 1750025. http://dx.doi.org/10.1142/s0129167x17500252.

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In this paper, an equality between the Hochs–Mathai type index and the Atiyah–Patodi–Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group actions. As a technical preparation, a problem concerning the Fredholm property of the global elliptic boundary value problems of the Atiyah–Patodi–Singer type on a non-compact manifold is studied.

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9

Singh, Vishal, Hossain Chizari, and Farzad Ismail. "Non-unified Compact Residual-Distribution Methods for Scalar Advection–Diffusion Problems." Journal of Scientific Computing 76, no. 3 (2018): 1521–46. http://dx.doi.org/10.1007/s10915-018-0674-1.

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10

Rahaman, Mijanur, and Rais Ahmad. "Weak and strong mixed vector equilibrium problems on non-compact domain." Journal of the Egyptian Mathematical Society 23, no. 2 (2015): 352–55. http://dx.doi.org/10.1016/j.joems.2014.06.007.

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11

Fieseler, K. H., and K. Tintarev. "Semilinear elliptic problems and concentration compactness on non-compact Riemannian manifolds." Journal of Geometric Analysis 13, no. 1 (2003): 67–75. http://dx.doi.org/10.1007/bf02930997.

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12

Molica Bisci, Giovanni, and Simone Secchi. "Elliptic problems on complete non-compact Riemannian manifolds with asymptotically non-negative Ricci curvature." Nonlinear Analysis 177 (December 2018): 637–72. http://dx.doi.org/10.1016/j.na.2018.04.019.

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13

DUC, DUONG MINH. "VARIATIONAL PROBLEMS OF CERTAIN FUNCTIONALS." International Journal of Mathematics 06, no. 04 (1995): 503–35. http://dx.doi.org/10.1142/s0129167x95000195.

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We get the existence and regularity of minimizers of certain functionals, which may be degenerate and have non-polynomial growth. Applying these results we can find exponentially harmonic maps in every homotopy class of maps from a connected Riemannian C4-manifold into [Formula: see text], where [Formula: see text] is a compact Riemannian C4-manifold.

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14

Bryantcev, I.I. "The dialogue between government and national and cultural public organizations: problems and prospects of their solving." Society and Power, no. 3 (June 5, 2009): 83–88. https://doi.org/10.5281/zenodo.13311754.

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The article grounds the role of national and cultural autonomy in the process of forming non-conflict interethnic relations and underlines the meaning of the autonomy as a real guarantee of development both compact living and non-compact living ethnic groups and formation of ethnic self-organization that allows to harmonize the state's unity with strengthening of ethnic unity, its self-expression.

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15

Wegert, E., and M. A. Efendiev. "Nonlinear Riemann—Hilbert problems with Lipschitz continuous boundary condition." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 4 (2000): 793–800. http://dx.doi.org/10.1017/s0308210500000421.

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Using a norm inequality for singular integral operators in pairs of weighted Lebesgue spaces we are able to prove existence and uniqueness results for solutions of nonlinear RiemannHilbert problems with non-compact Lipschitz continuous restriction curves.

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16

de Andrade, Bruno, and Claudio Cuevas. "Compact almost automorphic solutions to semilinear Cauchy problems with non-dense domain." Applied Mathematics and Computation 215, no. 8 (2009): 2843–49. http://dx.doi.org/10.1016/j.amc.2009.09.025.

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17

Fang, Yi. "Minimal annuli in R3 bounded by non-compact complete convex curves in parallel planes." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 3 (1996): 369–88. http://dx.doi.org/10.1017/s1446788700037885.

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AbstractIn this paper we consider the Plateau problem for surfaces of annular type bounded by a pair of convex, non-compact curves in parallel planes. We prove that for certain symmetric boundaries there are solutions to the non-compact Plateau problems (Theorem B). Except for boundaries consisting of a pair of parallel straight lines, these are the first known examples.

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18

Gérard, Patrick, and Sandrine Grellier. "Inverse spectral problems for compact Hankel operators." Journal of the Institute of Mathematics of Jussieu 13, no. 2 (2013): 273–301. http://dx.doi.org/10.1017/s1474748013000121.

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AbstractGiven two arbitrary sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $ of real numbers satisfying $$\begin{eqnarray*}\displaystyle \vert {\lambda }_{1} \vert \gt \vert {\mu }_{1} \vert \gt \vert {\lambda }_{2} \vert \gt \vert {\mu }_{2} \vert \gt \cdots \gt \vert {\lambda }_{j} \vert \gt \vert {\mu }_{j} \vert \rightarrow 0, &&\displaystyle\end{eqnarray*}$$ we prove that there exists a unique sequence $c= ({c}_{n} )_{n\in { \mathbb{Z} }_{+ } } $, real valued, such that the Hankel operators ${\Gamma }_{c} $ and ${\Gamma }_{\tilde {c} } $ of symbols $c= ({c}_

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19

Infante, Gennaro. "EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS." Proceedings of the Edinburgh Mathematical Society 46, no. 1 (2003): 75–86. http://dx.doi.org/10.1017/s0013091501001079.

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AbstractWorking on a suitable cone of continuous functions, we give new results for integral equations of the form $\lambda u(t)=\int_{G}k(t,s)f(s,u(s))\,\mathrm{d} s:=Tu(t)$, where $G$ is a compact set in $\mathbb{R}^{n}$ and $k$ is a possibly discontinuous function that is allowed to change sign. We apply our results to prove existence of eigenvalues of some non-local boundary-value problems.AMS 2000 Mathematics subject classification: Primary 34B10. Secondary 34B18; 47H10; 47H30

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20

S GARCIA, ELINO. "An Exploration of Synthetic Division for Non-Linear Polynomial Divisors." International Multidisciplinary Research Journal 4, no. 1 (2022): 11–21. http://dx.doi.org/10.54476/iimrj02.

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As a goal of developing alternative algorithm on division of polynomials whose dividend is 𝑎1𝑥 𝑛 + 𝑎2𝑥 𝑛−1 + 𝑎3𝑥 𝑛−2 + ⋯ + 𝑎𝑛𝑥 + 𝑎𝑛+1 and the divisor is 𝑏1𝑥 𝑚 + 𝑏2𝑥 𝑚−1 + 𝑏3𝑥 𝑚−2 … + 𝑏𝑚𝑥 + 𝑏𝑚+1, where 𝑛 > 𝑚, 𝑎1 ≠ 0, 𝑏1 ≠ 0, and 𝑎𝑖 ′𝑠and 𝑏𝑖 ′𝑠including 𝑎𝑛+1 and 𝑏𝑚+1 are constant, the researcher explored the synthetic division in compact form.The researcher believes that the algorithm in this study is a good alternative in dividing polynomials of higher degrees. In the said compact form, division of only some distinct pairs of non-linear polynomials were presented and served as reference prob

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21

an Huef, Astrid, S. Kaliszewski, and Iain Raeburn. "Extension problems and non-Abelian duality for C*-algebras." Bulletin of the Australian Mathematical Society 75, no. 2 (2007): 229–38. http://dx.doi.org/10.1017/s0004972700039162.

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Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

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22

Boffi, Daniele. "Finite element approximation of eigenvalue problems." Acta Numerica 19 (May 2010): 1–120. http://dx.doi.org/10.1017/s0962492910000012.

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We discuss the finite element approximation of eigenvalue problems associated with compact operators. While the main emphasis is on symmetric problems, some comments are present for non-self-adjoint operators as well. The topics covered include standard Galerkin approximations, non-conforming approximations, and approximation of eigenvalue problems in mixed form. Some applications of the theory are presented and, in particular, the approximation of the Maxwell eigenvalue problem is discussed in detail. The final part tries to introduce the reader to the fascinating setting of differential form

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23

Mazepa, E. A., and D. K. Ryaboshlykova. "Boundary-value problems for the inhomogeneous Schr"odinger equation with variations of its potential on non-compact Riemannian manifolds." Issues of Analysis 28, no. 3 (2021): 113–28. http://dx.doi.org/10.15393/j3.art.2021.10911.

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24

Mazepa, E. A., and D. K. Ryaboshlikova. "Symptotic behavior of solutions of the inhomogeneous Schrödinger equation on noncompact Riemannian manifolds." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 1 (February 12, 2024): 35–49. http://dx.doi.org/10.26907/0021-3446-2024-1-35-49.

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The paper studies the behavior of bounded solutions of the inhomogeneous Schrödinger equation on non-compact Riemannian manifolds under a variation of the right side of the equation. Various problems for homogeneous elliptic equations, in particular the Laplace-Beltrami equation and the stationary Schrödinger equation, have been considered by a number of Russian and foreign authors since the second half of the 20th century. In the first part of this paper, an approach to the formulation of boundary value problems based on the introduction of classes of equivalent functions will be developed. T

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25

S. Garcia, Elino. "An Exploration of Synthetic Division for Non-Linear Polynomial Divisors." International Multidisciplinary Research Journal 4, no. 1 (2022): 10–21. http://dx.doi.org/10.54476/1286801.

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As a goal of developing alternative algorithm on division of polynomials whose dividend is 𝑎1𝑥 𝑛 + 𝑎2𝑥 𝑛−1 + 𝑎3𝑥 𝑛−2 + ⋯ + 𝑎𝑛𝑥 + 𝑎𝑛+1 and the divisor is 𝑏1𝑥 𝑚 + 𝑏2𝑥 𝑚−1 + 𝑏3𝑥 𝑚−2 … + 𝑏𝑚𝑥 + 𝑏𝑚+1, where 𝑛 > 𝑚, 𝑎1 ≠ 0, 𝑏1 ≠ 0, and 𝑎𝑖 ′𝑠and 𝑏𝑖 ′𝑠including 𝑎𝑛+1 and 𝑏𝑚+1 are constant, the researcher explored the synthetic division in compact form.The researcher believes that the algorithm in this study is a good alternative in dividing polynomials of higher degrees. In the said compact form, division of only some distinct pairs of non-linear polynomials were presented and served as reference prob

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26

Hofmann, B., D. Düvelmeyer, and K. Krumbiegel. "APPROXIMATE SOURCE CONDITIONS IN TIKHONOV REGULARIZATION‐NEW ANALYTICAL RESULTS AND SOME NUMERICAL STUDIES." Mathematical Modelling and Analysis 11, no. 1 (2006): 41–56. http://dx.doi.org/10.3846/13926292.2006.9637301.

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We present some new ideas and results for finding convergence rates in Tikhonov regularization for ill‐posed linear inverse problems with compact and non‐compact forward operators based on the consideration of approximate source conditions and corresponding distance functions. The new results and studies complement and extend in numerous points the recent papers [5, 7, 8, 10] that also exploit the distance functions originally introduced in [2] which measure the violation of a moderate source condition that works as a benchmark. In this context, we distinguish as in [8] logarithmic, power and

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27

Geffner, Tomas, and Hector Geffner. "Compact Policies for Fully Observable Non-Deterministic Planning as SAT." Proceedings of the International Conference on Automated Planning and Scheduling 28 (June 15, 2018): 88–96. http://dx.doi.org/10.1609/icaps.v28i1.13880.

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Fully observable non-deterministic (FOND) planning is becoming increasingly important as an approach for computing proper policies in probabilistic planning, extended temporal plans in LTL planning, and general plans in generalized planning. In this work, we introduce a SAT encoding for FOND planning that is compact and can produce compact strong cyclic policies. Simple variations of the encodings are also introduced for strong planning and for what we call, dual FOND planning, where some non-deterministic actions are assumed to be fair (e.g., probabilistic) and others unfair (e.g., adversaria

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28

Gordin, V. A. "COMPACT FINITE-DIFFERENCE SCHEMES FOR WEAKLY NON-LINEAR PROBLEMS AND BOUNDARY CONDITIONS IMITATING CAUCHY PROBLEM." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (2019): 32–37. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).9.

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Compact finite-difference schemes are well known and provide high accuracy order for differential equation with constant coefficients. Algorithms for constructing compact schemes of the 4-th order for boundary value problems with variable (smooth or jump) coefficient are developed. For the diffusion equations with a smooth variable coefficient and the Levin – Leontovich equation, compact finite-difference schemes are also constructed and their 4-th order is experimentally confirmed. The method of constructing compact schemes of the 4-th order can be generalized to partial differential equation

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29

Ghimenti, Marco G., and Anna Maria Micheletti. "Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary." Mathematical Biosciences and Engineering 30, no. 4 (2022): 1209–35. http://dx.doi.org/10.3934/era.2022064.

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<abstract><p>We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature

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30

Sengupta, T. K., V. Lakshmanan, and V. V. S. N. Vijay. "A new combined stable and dispersion relation preserving compact scheme for non-periodic problems." Journal of Computational Physics 228, no. 8 (2009): 3048–71. http://dx.doi.org/10.1016/j.jcp.2009.01.003.

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31

Ignatyev, Mikhail. "Inverse scattering problem for Sturm-Liouville operator on non-compact A-graph. Uniqueness result." Tamkang Journal of Mathematics 46, no. 4 (2015): 401–22. http://dx.doi.org/10.5556/j.tkjm.46.2015.1806.

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We consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering problem for Sturm--Liouville differential operator with standard matching conditions in the internal vertices. Transport, spectral and scattering problems for differential operators on graphs appear frequently in mathematics, natural sciences and engineering. In particular, direct and inverse problems for such operators are used to construct and study models in mechanics, nano-electronics, quantum co

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32

Meskhi, Alexander. "On a measure of non-compactness for singular integrals." Journal of Function Spaces and Applications 1, no. 1 (2003): 35–43. http://dx.doi.org/10.1155/2003/927590.

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It is proved that there exists no weight pair(v, w)for which a singular integral operator is compact from the weighted Lebesgue spaceLwp(Rn)toLvp(Rn). Moreover, a measure of non-compatness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.

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33

Marraffa, Valeria, and Bianca Satco. "Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity." Mathematics 10, no. 1 (2021): 55. http://dx.doi.org/10.3390/math10010055.

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We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) i

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34

GOLODETS, VALENTIN YA, and SERGEY D. SINEL'SHCHIKOV. "On the conjugacy and isomorphism problems for stabilizers of Lie group actions." Ergodic Theory and Dynamical Systems 19, no. 2 (1999): 391–411. http://dx.doi.org/10.1017/s014338579913013x.

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The spaces of subgroups and Lie subalgebras with the group actions by conjugations are considered for real Lie groups. Our approach allows one to apply the properties of algebraically regular transformation groups to finding the conditions when those actions turn out to be type I. It follows, in particular, that in this case the stability groups for all the ergodic actions of such groups are conjugate (for example when the stability groups are compact). The isomorphism of the stability groups for ergodic actions is also established under some assumptions. A number of examples of non-conjugate

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35

Mazepa, Elena. "On Solvability of Boundary Value Problems of the Poisson Equation on Non-Compact Riemannian Manifolds." Vestnik Volgogradskogo gosudarstvennogo universiteta. Serija 1. Mathematical Physics and Computer Modeling 20, no. 3 (2017): 136–47. http://dx.doi.org/10.15688/mpcm.jvolsu.2017.3.10.

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36

Long, Guangqing, Xiaoyuan Huang, Aimei Tan, and Gnaneshwar Nelakanti. "Discrete product integration methods for eigen-problems of a class of non-compact integral operators." Applied Mathematics and Computation 219, no. 15 (2013): 7964–72. http://dx.doi.org/10.1016/j.amc.2013.02.034.

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37

Majidian, H., and E. Babolian. "An interpolation degenerate kernel method for eigenvalue problems of a class of non-compact operators." Applied Mathematics Letters 23, no. 8 (2010): 825–30. http://dx.doi.org/10.1016/j.aml.2010.01.019.

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38

Talgorn, Bastien, and Michael Kokkolaras. "Compact implementation of non-hierarchical analytical target cascading for coordinating distributed multidisciplinary design optimization problems." Structural and Multidisciplinary Optimization 56, no. 6 (2017): 1597–602. http://dx.doi.org/10.1007/s00158-017-1726-0.

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39

Aggarwal, Sudhanshu, Rishi Kumar, and Jyotsna Chandel. "Application of Rishi transform to the solution of nonlinear Volterra integral equation of the second kind ∗." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 42, no. 2 (2023): 186–93. http://dx.doi.org/10.48165/bpas.2023.42e.2.7.

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This paper aims to investigate the solution of non-linear Volterra integral equation of the second kind by using the Rishi transform. The solutions of two numerical problems in compact form are determined by applying the Rishi transform, which sug gests that the Rishi transform can be used as a tool for solving these and the other types of related real world problems across various disciplines.

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40

Ashton, Brenden, and Ian Doust. "A COMPARISON OF ALGEBRAS OF FUNCTIONS OF BOUNDED VARIATION." Proceedings of the Edinburgh Mathematical Society 49, no. 3 (2006): 575–91. http://dx.doi.org/10.1017/s0013091504001130.

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AbstractMotivated by problems in the spectral theory of linear operators, we previously introduced a new concept of variation for functions defined on a non-empty compact subset of the plane. In this paper, we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and compare these algebras with those previously used by Berkson and Gillespie in their theories of AC-operators and trigonometrically well-bounded operators.

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41

Dello Russo, Anahí, and Ana E. Alonso. "Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains." Computational Methods in Applied Mathematics 14, no. 1 (2014): 1–33. http://dx.doi.org/10.1515/cmam-2013-0014.

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Abstract. In this paper we present a theoretical framework for the analysis of the numerical approximations of a particular class of eigenvalue problems by mixed/hybrid methods. More precisely, we are interested in eigenproblems which are defined over curved domains or have internal curved boundaries and which may be associated with non-compact inverse operators. To do this, we consider external domain approximations $\Omega _{h}$ of the original domain $\Omega $, i.e., $\Omega _{h} \lnot \subset \Omega $. Sufficient conditions to ensure good convergence properties and optimal error bounds for

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42

Infante, Gennaro, and J. R. L. Webb. "NONLINEAR NON-LOCAL BOUNDARY-VALUE PROBLEMS AND PERTURBED HAMMERSTEIN INTEGRAL EQUATIONS." Proceedings of the Edinburgh Mathematical Society 49, no. 3 (2006): 637–56. http://dx.doi.org/10.1017/s0013091505000532.

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AbstractMotivated by some non-local boundary-value problems (BVPs) that arise in heat-flow problems, we establish new results for the existence of non-zero solutions of integral equations of the form$$ u(t)=\gamma(t)\alpha[u]+\int_{G}k(t,s)f(s,u(s))\,\mathrm{d}s, $$where $G$ is a compact set in $\mathbb{R}^{n}$. Here $\alpha[u]$ is a positive functional and $f$ is positive, while $k$ and $\gamma$ may change sign, so positive solutions need not exist. We prove the existence of multiple non-zero solutions of the BVPs under suitable conditions. We show that solutions of the BVPs lose positivity a

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43

Ashyralyev, Allaberen, and Ibrahim Mohammed Ibrahım. "High-Order, Accurate Finite Difference Schemes for Fourth-Order Differential Equations." Axioms 13, no. 2 (2024): 90. http://dx.doi.org/10.3390/axioms13020090.

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This article is devoted to the study of high-order, accurate difference schemes’ numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations with constant coefficients can be solved by classical integral transform methods. However, these classical methods can be used simply in the case when the differential equation has constant coefficients. We study fourth-order differential equations with dependent coefficients and their corresponding boundary value problems. Novel compact numer

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44

Shakarova, M. D. "Inverse problems for the subdiffusion equation." Uzbek Mathematical Journal 68, no. 3 (2024): 143–49. http://dx.doi.org/10.29229/uzmj.2024-3-14.

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In the Hilbert space H consider the subdiffusion equation Dtρu(t)+Au(t) = fg(t), ρ 2 (0; 1), t 2 (0; T]. In this equation A is an unbounded positive self-adjoint operator, Dtρ stands for the Caputo fractional derivative, g(t) 2 C[0; T] is a given function and f 2 H is an unknown element. It is assumed that A has a compact inverse A−1. The subdiffusion equation is studied with initial u(0) = ’ and non-local u(0) = u(T) conditions. To solve the inverse problem, an additional condition in the form u(t0) = , t0 2 (0; T) is taken. Here is a given element of H. The existence of a solution to these i

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CORRÊA, F. J. S. A., J. V. GONCALVES, and ANGELO RONCALLI. "ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS." Analysis and Applications 08, no. 02 (2010): 185–97. http://dx.doi.org/10.1142/s0219530510001576.

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We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

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Matevossian, Hovik. "On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces." Mathematical and Computational Applications 24, no. 1 (2019): 25. http://dx.doi.org/10.3390/mca24010025.

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We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a . Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space

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Matevossian, Hovik A. "Mixed Boundary Value Problems for the Elasticity System in Exterior Domains." Mathematical and Computational Applications 24, no. 2 (2019): 58. http://dx.doi.org/10.3390/mca24020058.

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We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.

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Liang, Yan, Xiao Ming Wu, Bi Hua Tang, and Yong Le Wu. "Compact LowPass Filter with Wide StopBand Using Non-Uniform Microstrip Resonant Cells." Applied Mechanics and Materials 263-266 (December 2012): 15–19. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.15.

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In this paper, a novel compact microstrip lowpass filter is designed. The proposed filter which is etched on the 50 Ω microstrip line consists of four non-uniform 1-D microstrip photonic bandgap (PBG) cells with different cutoff frequency.. The demonstration lowpass filter with 2.2 GHz cutoff frequency is designed, fabricated and measured. The measurement results show that the band rejection effect is better than -20 dB from 2.8 GHz to 10 GHz, the insertion is less than 2 dB, and the length of filter is 5.6 cm long. Compared with the conventional filter, the proposed filter has smaller size. M

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Friderikos, Orestis, Marc Olive, Emmanuel Baranger, Dimitris Sagris, and Constantine David. "A non-intrusive space-time interpolation from compact Stiefel manifolds of parametrized rigid-viscoplastic FEM problems." Computational Mechanics 68, no. 4 (2021): 861–83. http://dx.doi.org/10.1007/s00466-021-02050-0.

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Dai, Ruxin, Yin Wang, and Xiwei Wang. "Effects of Different High Order Compact Computations for Solving Boundary Layer Problems on Non-Uniform Grids." Journal of Computational Intelligence and Electronic Systems 3, no. 3 (2014): 200–211. http://dx.doi.org/10.1166/jcies.2014.1091.

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