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Journal articles on the topic 'Unbounded Coefficients'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Da Prato, G., and A. Ichikawa. "Riccati equations with unbounded coefficients." Annali di Matematica Pura ed Applicata 140, no. 1 (1985): 209–21. http://dx.doi.org/10.1007/bf01776850.

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2

Greco, Luigi, Gioconda Moscariello, and Teresa Radice. "Nondivergence elliptic equations with unbounded coefficients." Discrete & Continuous Dynamical Systems - B 11, no. 1 (2009): 131–43. http://dx.doi.org/10.3934/dcdsb.2009.11.131.

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3

Latushkin, Yuri, and Yuri Tomilov. "Fredholm differential operators with unbounded coefficients." Journal of Differential Equations 208, no. 2 (2005): 388–429. http://dx.doi.org/10.1016/j.jde.2003.10.018.

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4

Kudlak, Zachary, and R. Patrick Vernon. "Unbounded rational systems with nonconstant coefficients." Nonautonomous Dynamical Systems 9, no. 1 (2022): 307–16. http://dx.doi.org/10.1515/msds-2022-0160.

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Abstract We show the existence of unbounded solutions to difference equations of the form { x n + 1 = c ′ n x n B n y n , y n + 1 = b n x n + c n y n A n + C n y n f o r n = 0 , 1 , … , \left\{ {\matrix{{{x_{n + 1}} = {{{{c'}_n}{x_n}} \over {{B_n}{y_n}}},} \hfill \cr {{y_{n + 1}} = {{{b_n}{x_n} + {c_n}{y_n}} \over {{A_n} + {C_n}{y_n}}}} \hfill \cr } \,\,\,\,\,for} \right.\,\,\,n = 0,1, \ldots , where { c ′ n } n = 0 ∞ \left\{ {{{c'}_n}} \right\}_{n = 0}^\infty , { B ′ n } n = 0 ∞ \left\{ {{{B'}_n}} \right\}_{n = 0}^\infty , { b n } n = 0 ∞ \left\{ {{b_n}} \right\}_{n = 0}^\infty , { c n } n =

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5

Jadlovská, Irena, George E. Chatzarakis, and Ercan Tunç. "Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients." Mathematica Slovaca 74, no. 3 (2024): 637–64. http://dx.doi.org/10.1515/ms-2024-0049.

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Abstract In this paper, we initiate the study of asymptotic and oscillatory properties of solutions to second-order functional differential equations with noncanonical operators and unbounded neutral coefficients, using a recent method of iteratively improved monotonicity properties of nonoscillatory solutions. Our results rely on ideas that essentially improve standard techniques for the investigation of differential equations with unbounded neutral terms with delay or advanced argument. The core of the method is presented in a form that suggests further generalizations for higher-order diffe

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6

Kusano, Takaŝi, and Marko Švec. "On unbounded positive solutions of nonlinear differential equations with oscillating coefficients." Czechoslovak Mathematical Journal 39, no. 1 (1989): 133–41. http://dx.doi.org/10.21136/cmj.1989.102285.

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7

Owino, Benard, Fredrick Nyamwala, and David Ambogo. "Stability of Krein-von Neumann self-adjoint operator extension under unbounded perturbations." Annals of Mathematics and Computer Science 23 (April 26, 2024): 29–47. http://dx.doi.org/10.56947/amcs.v23.300.

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We have considered a fourth order difference operator defined on the Hilbert space of square summable sequences on N. We investigated the stability of existence of Krein-von Neumann self-adjoint extension of difference operators under bounded and unbounded coefficients. Using asymptotic summation based on discretised Levinson's theorem and appropriate smoothness and decay conditions, we have shown that unlike the case of deficiency indices and discrete spectrum, the existence of positive self-adjoint operator extensions is stable under unbounded perturbations. These results now exhaustively ch

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8

Gashi, Bujar, and Jiajie Li. "Integrability of exponential process and its application to backward stochastic differential equations." IMA Journal of Management Mathematics 30, no. 4 (2018): 335–65. http://dx.doi.org/10.1093/imaman/dpy008.

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Abstract We consider the integrability problem of an exponential process with unbounded coefficients. The integrability is established under weaker conditions of Kazamaki type, which complements the results of Yong obtained under a Novikov type condition. As applications, we consider the solvability of linear backward stochastic differential equations (BSDEs) and market completeness, the solvability of a Riccati BSDE and optimal investment, all in the setting of unbounded coefficients.

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9

Czornik, Adam, and Michał Niezabitowski. "Lyapunov exponents for systems with unbounded coefficients." Dynamical Systems 28, no. 2 (2013): 140–53. http://dx.doi.org/10.1080/14689367.2012.742038.

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10

Kunze, Markus, Luca Lorenzi, and Alessandra Lunardi. "Nonautonomous Kolmogorov parabolic equations with unbounded coefficients." Transactions of the American Mathematical Society 362, no. 01 (2009): 169–98. http://dx.doi.org/10.1090/s0002-9947-09-04738-2.

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11

Lorenzi, Luca, and Alessandro Zamboni. "Cores for parabolic operators with unbounded coefficients." Journal of Differential Equations 246, no. 7 (2009): 2724–61. http://dx.doi.org/10.1016/j.jde.2008.12.015.

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12

Zalygina, V. I. "Lyapunov Equivalence of Systems with Unbounded Coefficients." Journal of Mathematical Sciences 210, no. 2 (2015): 210–16. http://dx.doi.org/10.1007/s10958-015-2558-3.

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13

Cicognani, Massimo. "Coefficients with unbounded derivatives in hyperbolic equations." Mathematische Nachrichten 276, no. 1 (2004): 31–46. http://dx.doi.org/10.1002/mana.200310210.

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14

Da Prato, Giuseppe, and Beniamin Goldys. "Elliptic Operators on Rd with Unbounded Coefficients." Journal of Differential Equations 172, no. 2 (2001): 333–58. http://dx.doi.org/10.1006/jdeq.2000.3866.

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15

Yang, Yang. "An Improved Unbounded-DP Algorithm for the Unbounded Knapsack Problem with Bounded Coefficients." Mathematics 12, no. 12 (2024): 1878. http://dx.doi.org/10.3390/math12121878.

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Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range R, and these instances can be referred to as the unbounded knapsack problem with bounded coefficients (UKPB). In order to increase the difficulty of solving these instances, the knapsack capacity C is usually set to a very large value. While current efficient algorithms primarily center on the Fast Fourier Transform (FFT) and (min,+)-convolution method, there is a simpler method worth considering. In this paper, based on the basic Unbounded-DP algorithm, w

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16

Dong, Wei, and Yihong Du. "Unbounded principal eigenfunctions and the logistic equation on RN." Bulletin of the Australian Mathematical Society 67, no. 3 (2003): 413–27. http://dx.doi.org/10.1017/s0004972700037229.

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We consider the logistic equation − Δu = a (x) u − b (x) up on all of RN with possibly unbounded coefficients near infinity. We show that under suitable growth conditions of the coefficients, the behaviour of the positive solutions of the logistic equation can be largely determined. We also show that certain linear eigenvalue problems on all of RN have principal eigenfunctions that become unbounded near infinity at an exponential rate. Using these results, we finally show that the logistic equation has a unique positive solution under suitable growth restrictions for its coefficients.

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17

Motreanu, Dumitru, and Elisabetta Tornatore. "Dirichlet problems with anisotropic principal part involving unbounded coefficients." Electronic Journal of Differential Equations 2024, no. 01-?? (2024): 11. http://dx.doi.org/10.58997/ejde.2024.11.

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This article establishes the existence of solutions in a weak sense for a quasilinear Dirichlet problem exhibiting anisotropic differential operator with unbounded coefficients in the principal part and full dependence on the gradient in the lower order terms. A major part of this work focuses on the existence of a uniform bound for the solution set in the anisotropic setting. The unbounded coefficients are handled through an appropriate truncation and a priori estimates. For more information see https://ejde.math.txstate.edu/Volumes/2024/11/abstr.html

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18

Bayandiyev, Ye N. "About the Storm-Liouville operator with negative parameter in space L2(R)." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 80, no. 2 (2021): 34–40. http://dx.doi.org/10.47533/2020.1606-146x.82.

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In this paper, the question of the existence of a resolvent is studied, and also, after closure in space, the smoothness of functions from the domain of an operator of the unbounded type in an unbounded domain with coefficients strongly increasing at infinity is investigated.

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19

Bertoldi, M., and S. Fornaro. "Gradient estimates in parabolic problems with unbounded coefficients." Studia Mathematica 165, no. 3 (2004): 221–54. http://dx.doi.org/10.4064/sm165-3-3.

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20

Florchinger, Patrick, and Giovanna Nappo. "Continuity of the Filter with Unbounded Observation Coefficients." Stochastic Analysis and Applications 29, no. 4 (2011): 612–30. http://dx.doi.org/10.1080/07362994.2011.581087.

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21

Czornik, Adam, and Michal Niezabitowski. "Corrigendum Lyapunov exponents for systems with unbounded coefficients." Dynamical Systems 28, no. 2 (2013): 299. http://dx.doi.org/10.1080/14689367.2012.756700.

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22

Fagnola, Franco, and Stephen J. Wills. "Solving quantum stochastic differential equations with unbounded coefficients." Journal of Functional Analysis 198, no. 2 (2003): 279–310. http://dx.doi.org/10.1016/s0022-1236(02)00089-7.

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23

Aptekarev, A. I., and J. S. Geronimo. "Measures for orthogonal polynomials with unbounded recurrence coefficients." Journal of Approximation Theory 207 (July 2016): 339–47. http://dx.doi.org/10.1016/j.jat.2016.02.009.

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24

Filinovskii, A. V. "Hyperbolic Equations with Growing Coefficients in Unbounded Domains." Journal of Mathematical Sciences 197, no. 3 (2014): 435–46. http://dx.doi.org/10.1007/s10958-014-1725-2.

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25

Shiryaev, K. E. "Central Exponent of a System with Unbounded Coefficients." Journal of Mathematical Sciences 210, no. 3 (2015): 331–32. http://dx.doi.org/10.1007/s10958-015-2568-1.

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26

Gy�ngy, Istv�n, and Nicolai V. Krylov. "On stochastic partial differential equations with Unbounded coefficients." Potential Analysis 1, no. 3 (1992): 233–56. http://dx.doi.org/10.1007/bf00269509.

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27

Metafune, Giorgio, and Chiara Spina. "A degenerate elliptic operator with unbounded diffusion coefficients." Rendiconti Lincei - Matematica e Applicazioni 25, no. 2 (2014): 109–40. http://dx.doi.org/10.4171/rlm/670.

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28

Angiuli, Luciana, and Luca Lorenzi. "On coupled systems of PDEs with unbounded coefficients." Dynamics of Partial Differential Equations 17, no. 2 (2020): 129–63. http://dx.doi.org/10.4310/dpde.2020.v17.n2.a3.

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29

Escauriaza, Luis, and Steve Hofmann. "Kato square root problem with unbounded leading coefficients." Proceedings of the American Mathematical Society 146, no. 12 (2018): 5295–310. http://dx.doi.org/10.1090/proc/14224.

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30

Fagnola, Franco. "On quantum stochastic differential equations with unbounded coefficients." Probability Theory and Related Fields 86, no. 4 (1990): 501–16. http://dx.doi.org/10.1007/bf01198172.

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31

Kogut, P. I. "A Note on Some Properties of Unbounded Bilinear Forms Associated with Skew-Symmetric $L^q(\Omega)$-Matrices." Researches in Mathematics 32, no. 1 (2024): 83. http://dx.doi.org/10.15421/242407.

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We study the bilinear forms on the space of measurable $p$-integrable functions which are generated by skew-symmetric matrices with unbounded coefficients. We give an example showing that if a skew-symmetric matrix contains a locally unbounded $L^q$-elements, then the corresponding quadratic forms can be alternating. These questions are closely related to the existence issues of the Nuemann boundary value problem for $p$-Laplace elliptic equations with non-symmetric and locally unbounded anisotropic diffusion matrices.

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32

Muratbekov, Mussakan, and Yerik Bayandiyev. "On the resolvent existence and the separability of a hyperbolic operator with fast growing coefficients in L2(R2)." Filomat 35, no. 3 (2021): 707–21. http://dx.doi.org/10.2298/fil2103707m.

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This paper studies the question of the resolvent existence, as well as, the smoothness of elements from the definition domain (separability) of a class of hyperbolic differential operators defined in an unbounded domain with greatly increasing coefficients after a closure in the space L2(R2). Such a problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that a detailed analysis shows that when studying the spectral properties of differential operators specified in an unbounded domain, the behavior of the coefficients at infinity plays an important role.

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33

Kumar, M. Sathish, R. Elayaraja, V. Ganesan, Omar Bazighifan, Khalifa Al-Shaqsi, and Kamsing Nonlaopon. "Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order." Fractal and Fractional 5, no. 3 (2021): 95. http://dx.doi.org/10.3390/fractalfract5030095.

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New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

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34

Chicco, Maurizio, and Marina Venturino. "Dirichlet problem for a divergence form elliptic equation with unbounded coefficients in an unbounded domain." Annali di Matematica Pura ed Applicata 178, no. 1 (2000): 325–38. http://dx.doi.org/10.1007/bf02505902.

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35

Fornaro, Simona, Nicola Fusco, Giorgio Metafune, and Diego Pallara. "Sharp upper bounds for the density of some invariant measures." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, no. 6 (2009): 1145–61. http://dx.doi.org/10.1017/s0308210508000498.

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36

Baskakov, A. G., and V. B. Didenko. "Spectral analysis of differential operators with unbounded periodic coefficients." Differential Equations 51, no. 3 (2015): 325–41. http://dx.doi.org/10.1134/s0012266115030052.

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37

Cherepova, M. F. "The Cauchy problem for parabolic equations with unbounded coefficients." Doklady Mathematics 91, no. 3 (2015): 364–66. http://dx.doi.org/10.1134/s1064562415030254.

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38

Vlasov, V. V., and N. A. Rautian. "Study of functional-differential equations with unbounded operator coefficients." Doklady Mathematics 96, no. 3 (2017): 620–24. http://dx.doi.org/10.1134/s1064562417060291.

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39

Orsina, Luigi. "Existence results for some elliptic equations with unbounded coefficients." Asymptotic Analysis 34, no. 3-4 (2003): 187–98. https://doi.org/10.3233/asy-2003-544.

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40

Manca, Luigi. "Fokker–Planck Equation for Kolmogorov Operators with Unbounded Coefficients." Stochastic Analysis and Applications 27, no. 4 (2009): 747–69. http://dx.doi.org/10.1080/07362990902976579.

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41

Da Prato, Giuseppe, and Vincenzo Vespri. "Maximal Lp regularity for elliptic equations with unbounded coefficients." Nonlinear Analysis: Theory, Methods & Applications 49, no. 6 (2002): 747–55. http://dx.doi.org/10.1016/s0362-546x(01)00133-x.

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42

Della Pietra, Francesco, and Giuseppina di Blasio. "Existence results for nonlinear elliptic problems with unbounded coefficients." Nonlinear Analysis: Theory, Methods & Applications 71, no. 1-2 (2009): 72–87. http://dx.doi.org/10.1016/j.na.2008.10.047.

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43

Castro Santis, Ricardo, and Alberto Barchielli. "Quantum stochastic differential equations and continuous measurements: unbounded coefficients." Reports on Mathematical Physics 67, no. 2 (2011): 229–54. http://dx.doi.org/10.1016/s0034-4877(11)80014-5.

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44

Monsurrò, Sara, and Maria Transirico. "Noncoercive elliptic equations with discontinuous coefficients in unbounded domains." Nonlinear Analysis 163 (November 2017): 86–103. http://dx.doi.org/10.1016/j.na.2017.07.008.

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45

Candela, A. M., and A. Salvatore. "Normal geodesics in stationary Lorentzian manifolds with unbounded coefficients." Journal of Geometry and Physics 44, no. 2-3 (2002): 171–95. http://dx.doi.org/10.1016/s0393-0440(02)00060-8.

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46

Geronimo, Jeffrey S., and Walter Van Assche. "Relative asymptotics for orthogonal polynomials with unbounded recurrence coefficients." Journal of Approximation Theory 62, no. 1 (1990): 47–69. http://dx.doi.org/10.1016/0021-9045(90)90046-s.

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47

Assing, Sigurd, and Ralf Manthey. "Invariant measures for stochastic heat equations with unbounded coefficients." Stochastic Processes and their Applications 103, no. 2 (2003): 237–56. http://dx.doi.org/10.1016/s0304-4149(02)00211-9.

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48

Zhang, Xicheng. "Stochastic partial differential equations with unbounded and degenerate coefficients." Journal of Differential Equations 250, no. 4 (2011): 1924–66. http://dx.doi.org/10.1016/j.jde.2010.11.021.

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49

Chebotarev, A. M., J. C. Garcia, and R. B. Quezada. "On the lindblad equation with unbounded time-dependent coefficients." Mathematical Notes 61, no. 1 (1997): 105–17. http://dx.doi.org/10.1007/bf02355012.

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50

Böttcher, Björn. "On the construction of Feller processes with unbounded coefficients." Electronic Communications in Probability 16 (2011): 545–55. http://dx.doi.org/10.1214/ecp.v16-1652.

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