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Journal articles on the topic 'Neumann problems'

Author: Grafiati

Published: 14 March 2023

Last updated: 19 July 2025

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1

Manning, Robert S. "Conjugate Points Revisited and Neumann–Neumann Problems." SIAM Review 51, no. 1 (2009): 193–212. http://dx.doi.org/10.1137/060668547.

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2

Szajewska, Marzena, and Agnieszka Tereszkiewicz. "TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS." Acta Polytechnica 56, no. 3 (2016): 245. http://dx.doi.org/10.14311/ap.2016.56.0245.

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Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

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3

Gasiński, Leszek, Liliana Klimczak, and Nikolaos S. Papageorgiou. "Nonlinear noncoercive Neumann problems." Communications on Pure and Applied Analysis 15, no. 4 (2016): 1107–23. http://dx.doi.org/10.3934/cpaa.2016.15.1107.

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4

Mugnai, Dimitri, and Edoardo Proietti Proietti Lippi. "Quasilinear Fractional Neumann Problems." Mathematics 13, no. 1 (2024): 85. https://doi.org/10.3390/math13010085.

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We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, even in the linear case, for which no regularity can indeed be assumed.

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5

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Anisotropic nonlinear Neumann problems." Calculus of Variations and Partial Differential Equations 42, no. 3-4 (2011): 323–54. http://dx.doi.org/10.1007/s00526-011-0390-2.

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6

Motreanu, D., V. V. Motreanu, and N. S. Papageorgiou. "On resonant Neumann problems." Mathematische Annalen 354, no. 3 (2011): 1117–45. http://dx.doi.org/10.1007/s00208-011-0763-z.

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7

Nittka, Robin. "Inhomogeneous parabolic Neumann problems." Czechoslovak Mathematical Journal 64, no. 3 (2014): 703–42. http://dx.doi.org/10.1007/s10587-014-0127-4.

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8

Dudko, Anastasia, and Vyacheslav Pivovarchik. "Three spectra problem for Stieltjes string equation and Neumann conditions." Proceedings of the International Geometry Center 12, no. 1 (2019): 41–55. http://dx.doi.org/10.15673/tmgc.v12i1.1367.

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Spectral problems are considered which appear in description of small transversal vibrations of Stieltjes strings. It is shown that the eigenvalues of the Neumann-Neumann problem, i.e. the problem with the Neumann conditions at both ends of the string interlace with the union of the spectra of the Neumann-Dirichlet problems, i.e. problems with the Neumann condition at one end and Dirichlet condition at the other end on two parts of the string. It is shown that the spectrum of Neumann-Neumann problem on the whole string, the spectrum of Neumann-Dirichlet problem on the left part of the string, all but one eigenvalues of the Neumann-Dirichlet problem on the right part of the string and total masses of the parts uniquely determine the masses and the intervals between them.

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9

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Nonlinear Neumann Problems with Constraints." Funkcialaj Ekvacioj 56, no. 2 (2013): 249–70. http://dx.doi.org/10.1619/fesi.56.249.

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10

Motreanu, D., V. V. Motreanu, and N. S. Papageorgiou. "Nonlinear Neumann problems near resonance." Indiana University Mathematics Journal 58, no. 3 (2009): 1257–80. http://dx.doi.org/10.1512/iumj.2009.58.3565.

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11

Ferone, V., and A. Mercaldo. "Neumann Problems and Steiner Symmetrization." Communications in Partial Differential Equations 30, no. 10 (2005): 1537–53. http://dx.doi.org/10.1080/03605300500299596.

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12

Bramanti, Marco. "Symmetrization in parabolic neumann problems." Applicable Analysis 40, no. 1 (1991): 21–39. http://dx.doi.org/10.1080/00036819008839990.

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13

Aizicovici, Sergiu, Nikolaos S. Papageorgiou, and Vasile Staicu. "Nonlinear, nonhomogeneous parametric Neumann problems." Topological Methods in Nonlinear Analysis 48, no. 1 (2016): 1. http://dx.doi.org/10.12775/tmna.2016.035.

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14

Candito, Pasquale, Roberto Livrea, and Nikolaos Papageorgiou. "Nonlinear nonhomogeneous Neumann eigenvalue problems." Electronic Journal of Qualitative Theory of Differential Equations, no. 46 (2015): 1–24. http://dx.doi.org/10.14232/ejqtde.2015.1.46.

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15

Cianchi, Andrea, and Vladimir G. Maz'ya. "Neumann problems and isocapacitary inequalities." Journal de Mathématiques Pures et Appliquées 89, no. 1 (2008): 71–105. http://dx.doi.org/10.1016/j.matpur.2007.10.001.

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16

Volzone, Bruno. "Symmetrization for fractional Neumann problems." Nonlinear Analysis: Theory, Methods & Applications 147 (December 2016): 1–25. http://dx.doi.org/10.1016/j.na.2016.08.029.

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17

Rachůnková, Irena, Svatoslav Staněk, Ewa Weinmüller, and Michael Zenz. "Neumann problems with time singularities." Computers & Mathematics with Applications 60, no. 3 (2010): 722–33. http://dx.doi.org/10.1016/j.camwa.2010.05.019.

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18

Qiu, Guohuan, and Chao Xia. "Classical Neumann Problems for Hessian Equations and Alexandrov–Fenchel’s Inequalities." International Mathematics Research Notices 2019, no. 20 (2018): 6285–303. http://dx.doi.org/10.1093/imrn/rnx296.

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Abstract Recently, the 1st named author together, with Xinan Ma [12], has proved the existence of the Neumann problems for Hessian equations. In this paper, we proceed further to study classical Neumann problems for Hessian equations. We prove here the existence of classical Neumann problems for uniformly convex domains in $\mathbb {R}^{n}$. As an application, we use the solution of the classical Neumann problem to give a new proof of a family of Alexandrov–Fenchel inequalities arising from convex geometry. This geometric application is motivated by Reilly [18].

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19

Fiacca, Antonella, and Raffaella Servadei. "Extremal solutions for nonlinear neumann problems." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 21, no. 2 (2001): 191. http://dx.doi.org/10.7151/dmdico.1024.

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20

López, Ginés, and Juan-Aurelio Montero-Sánchez. "Neumann boundary value problems across resonance." ESAIM: Control, Optimisation and Calculus of Variations 12, no. 3 (2006): 398–408. http://dx.doi.org/10.1051/cocv:2006009.

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21

Pomponio, Alessio. "Singularly perturbed Neumann problems with potentials." Topological Methods in Nonlinear Analysis 23, no. 2 (2004): 301. http://dx.doi.org/10.12775/tmna.2004.013.

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22

Fan, Xianling. "Eigenvalues of the -Laplacian Neumann problems." Nonlinear Analysis: Theory, Methods & Applications 67, no. 10 (2007): 2982–92. http://dx.doi.org/10.1016/j.na.2006.09.052.

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23

Kristály, Alexandru. "Perturbed Neumann Problems with Many Solutions." Numerical Functional Analysis and Optimization 29, no. 9-10 (2008): 1114–27. http://dx.doi.org/10.1080/01630560802418383.

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24

Papalini, Francesca. "Nonlinear eigenvalue Neumann problems with discontinuities." Journal of Mathematical Analysis and Applications 273, no. 1 (2002): 137–52. http://dx.doi.org/10.1016/s0022-247x(02)00222-6.

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25

Halidias, N. "Neumann boundary value problems with discontinuities." Applied Mathematics Letters 16, no. 5 (2003): 729–32. http://dx.doi.org/10.1016/s0893-9659(03)00074-0.

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26

Buttazzo, Giuseppe, and Franco Tomarelli. "Compatibility conditions for nonlinear Neumann problems." Advances in Mathematics 89, no. 2 (1991): 127–43. http://dx.doi.org/10.1016/0001-8708(91)90076-j.

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27

Hu, Shouchuan, and N. S. Papageorgiou. "Nonlinear elliptic problems of Neumann-type." Rendiconti del Circolo Matematico di Palermo 50, no. 1 (2001): 47–66. http://dx.doi.org/10.1007/bf02843918.

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28

Pan, Xing-Bin. "Singular limit of quasilinear Neumann problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 205–23. http://dx.doi.org/10.1017/s0308210500030845.

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This paper is devoted to the study of the singular limit of the minimal solutions, as p → 1, of quasilinear Neumann problems involving p-Laplacian operators. It is established that the limit function is of bounded variation and is locally Höolder-continuous inside the domain.

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29

Filippakis, Michael, Leszek Gasiński, and Nikolaos S. Papageorgiou. "Multiplicity Results for Nonlinear Neumann Problems." Canadian Journal of Mathematics 58, no. 1 (2006): 64–92. http://dx.doi.org/10.4153/cjm-2006-004-6.

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AbstractIn this paper we study nonlinear elliptic problems of Neumann type driven by the p-Laplacian differential operator. We look for situations guaranteeing the existence of multiple solutions. First we study problems which are strongly resonant at infinity at the first (zero) eigenvalue. We prove five multiplicity results, four for problems with nonsmooth potential and one for problems with a C1-potential. In the last part, for nonsmooth problems in which the potential eventually exhibits a strict super-p-growth under a symmetry condition, we prove the existence of infinitely many pairs of nontrivial solutions. Our approach is variational based on the critical point theory for nonsmooth functionals. Also we present some results concerning the first two elements of the spectrum of the negative p-Laplacian with Neumann boundary condition.

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30

Dipierro, Serena, Xavier Ros-Oton, and Enrico Valdinoci. "Nonlocal problems with Neumann boundary conditions." Revista Matemática Iberoamericana 33, no. 2 (2017): 377–416. http://dx.doi.org/10.4171/rmi/942.

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31

Taira, Kazuaki. "Logistic Neumann problems with discontinuous coefficients." ANNALI DELL'UNIVERSITA' DI FERRARA 66, no. 2 (2020): 409–85. http://dx.doi.org/10.1007/s11565-020-00350-6.

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32

Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Neumann problems for nonlinear hemivariational inequalities." Mathematische Nachrichten 280, no. 3 (2007): 290–301. http://dx.doi.org/10.1002/mana.200410482.

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33

Serra, Enrico, and Paolo Tilli. "Monotonicity constraints and supercritical Neumann problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 28, no. 1 (2011): 63–74. http://dx.doi.org/10.1016/j.anihpc.2010.10.003.

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34

Liu, Zhen-hai, and Nikolaos S. Papageorgiou. "Parametric Anisotropic (p, q)-Neumann Problems." Acta Mathematicae Applicatae Sinica, English Series 39, no. 4 (2023): 926–42. http://dx.doi.org/10.1007/s10255-023-1087-y.

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35

Urquhart, Alasdair. "Von Neumann, Gödel and Complexity Theory." Bulletin of Symbolic Logic 16, no. 4 (2010): 516–30. http://dx.doi.org/10.2178/bsl/1294171130.

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AbstractAround 1989, a striking letter written in March 1956 from Kurt Gödel to John von Neumann came to light. It poses some problems about the complexity of algorithms; in particular, it asks a question that can be seen as the first formulation of the P = ? NP question. This paper discusses some of the background to this letter, including von Neumann's own ideas on complexity theory. Von Neumann had already raised explicit questions about the complexity of Tarski's decision procedure for elementary algebra and geometry in a letter of 1949 to J. C. C. McKinsey. The paper concludes with a discussion of why theoretical computer science did not emerge as a separate discipline until the 1960s.

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36

Dassios, G., and A. S. Fokas. "The basic elliptic equations in an equilateral triangle." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2061 (2005): 2721–48. http://dx.doi.org/10.1098/rspa.2005.1466.

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In his deep and prolific investigations of heat diffusion, Lamé was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular, he derived explicit results for the Dirichlet and Neumann cases using an ingenious change of variables. The relevant eigenfunctions are a complicated infinite series in terms of his variables. Here we first show that boundary-value problems with simple boundary conditions, such as the Dirichlet and the Neumann problems, can be solved in an elementary manner. In particular, the unknown Neumann and Dirichlet boundary values can be expressed in terms of a Fourier series for the Dirichlet and the Neumann problems, respectively. Our analysis is based on the so-called global relation, which is an algebraic equation coupling the Dirichlet and the Neumann spectral values on the perimeter of the triangle. As Lamé correctly pointed out, infinite series are inadequate for expressing the solution of more complicated problems such as mixed boundary-value problems. In this paper we show, further utilizing the global relation, that such problems can be solved in terms of generalized Fourier integrals .

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37

Le Tallec, Patrick, Jan Mandel, and Marina Vidrascu. "A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems." SIAM Journal on Numerical Analysis 35, no. 2 (1998): 836–67. http://dx.doi.org/10.1137/s0036142995291019.

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38

Heinkenschloss, Matthias, and Hoang Nguyen. "Neumann--Neumann Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems." SIAM Journal on Scientific Computing 28, no. 3 (2006): 1001–28. http://dx.doi.org/10.1137/040612774.

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39

Mukminov, Farit Khamzaevich, and Oleg Sergeevich Stekhun. "Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure - valued potential." Ufa Mathematical Journal 16, no. 4 (2024): 53–75. https://doi.org/10.13108/2024-16-4-53.

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In the exterior of a ball in the space $\mathbb{R}^n$ we consider the Zaremba and Neumann problems for quasilinear second order elliptic problems with a measure - valued potential. We proved the existence and uniqueness of entropy solution to the Zaremba and Neumann problems.

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40

Vasilyev, Vladimir. "On the Dirichlet and Neumann problems in multi-dimensional cone." Mathematica Bohemica 139, no. 2 (2014): 333–40. http://dx.doi.org/10.21136/mb.2014.143858.

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41

Pivovarchik, Vyacheslav. "On Ambarzumian type theorems for tree domains." Opuscula Mathematica 42, no. 3 (2022): 427–37. http://dx.doi.org/10.7494/opmath.2022.42.3.427.

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It is known that the spectrum of the spectral Sturm-Liouville problem on an equilateral tree with (generalized) Neumann's conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials on the edges (Ambarzumian's theorem). This case is exceptional, and in general case (when the Dirichlet conditions are imposed at some of the pendant vertices) even two spectra of spectral problems do not determine uniquely the potentials on the edges. We consider the spectral Sturm-Liouville problem on an equilateral tree rooted at its pendant vertex with (generalized) Neumann conditions at all vertices except of the root and the Dirichlet condition at the root. In this case Ambarzumian's theorem can't be applied. We show that if the spectrum of this problem is unperturbed, the spectrum of the Neumann-Dirichlet problem on the root edge is also unperturbed and the spectra of the problems on the complimentary subtrees with (generalized) Neumann conditions at all vertices except the subtrees' roots and the Dirichlet condition at the subtrees' roots are unperturbed then the potential on each edge of the tree is 0 almost everywhere.

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42

Keanini, R. G. "Random walk methods for scalar transport problems subject to Dirichlet, Neumann and mixed boundary conditions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2078 (2006): 435–60. http://dx.doi.org/10.1098/rspa.2006.1769.

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Three stochastic-based methods are proposed for solving unsteady scalar transport problems in bounded, single-phase domains. The first (Method I), a local solution appropriate to problems having Dirichlet conditions, adapts a well-known local stochastic solution of a backward Fokker–Planck equation to scalar transport. Method II, a local solution applicable to Dirichlet, Neumann and/or mixed initial boundary value problems (IBVPs), and representing a time-dependent extension of a recently reported heuristic steady solution, provides a straightforward addition to the limited collection of techniques available for Neumann and mixed problems. This approach is shown to be equivalent to a long-standing, rigorous low-order solution and, in addition, allows development of a probabilistic-based analytical solution to Neumann problems, stated in terms of an exit probability. Method III, a global solution, likewise suitable for Neumann and mixed IBVPs, follows by combined application of domain boundary Taylor expansions and Method I. This approach is shown to be computationally equivalent to a global version of Method II.

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43

Burgumbayeva, S. K., D. I. Tungushbayeva, M. Aldai, and B. S. Hurimov. "Boundary value problems for the harmonic differential equations of the third order." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 92, no. 2 (2024): 161–78. http://dx.doi.org/10.47533/2024.1606-146x.35.

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The study of the main boundary value problems for complex partial differential equations of any order is limited to model equations. Four main boundary value problems are investigated on the unit disk, namely the Schwarz, Dirichlet, Neumann, Robin problems for analytical functions and more generally for the inhomogeneous Cauchy-Riemann equation. The article considers and proves the properties of Dirichlet and Neumann boundary value problems for three-harmonic functions in a unit disc. The representation of solutions and the conditions of solvability are given explicitly. The fundamental tools are the Gauss theorem and the Cauchy-Pompey representation, as well as Dirichlet and Neumann problems for bi-harmonic equations on a unit circle.

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44

Ko, Y. Y. "Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems." Journal of Mechanics 36, no. 6 (2020): 749–61. http://dx.doi.org/10.1017/jmech.2020.15.

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ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

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45

Karachik, Valery, Batirkhan Turmetov, and Hongfen Yuan. "Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball." Mathematics 10, no. 7 (2022): 1158. http://dx.doi.org/10.3390/math10071158.

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Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann boundary value problems are studied. For the problems under consideration, existence and uniqueness theorems are proved. Necessary and sufficient conditions for the solvability of all problems are obtained and an integral representations of solutions are given in terms of the corresponding Green’s functions.

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46

Goldfeld, Paulo, Luca F. Pavarino, and Olof B. Widlund. "Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity." Numerische Mathematik 95, no. 2 (2003): 283–324. http://dx.doi.org/10.1007/s00211-002-0450-9.

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47

Dryja, Maksymilian, and Olof B. Widlund. "Schwarz methods of neumann-neumann type for three-dimensional elliptic finite element problems." Communications on Pure and Applied Mathematics 48, no. 2 (1995): 121–55. http://dx.doi.org/10.1002/cpa.3160480203.

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48

Th. Kyritsi, Sophia, and Nikolaos S. Papageorgiou. "Multiple solutions for nonlinear coercive Neumann problems." Communications on Pure & Applied Analysis 8, no. 6 (2009): 1957–74. http://dx.doi.org/10.3934/cpaa.2009.8.1957.

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49

Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Nonlinear Neumann problems with asymmetric nonsmooth potential." Bulletin of the Belgian Mathematical Society - Simon Stevin 12, no. 3 (2005): 417–33. http://dx.doi.org/10.36045/bbms/1126195346.

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50

Jankowski, Tadeusz. "Existence and approximate solutions of Neumann problems." Integral Transforms and Special Functions 14, no. 5 (2003): 429–36. http://dx.doi.org/10.1080/1065246031000081625.

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