On resonant Neumann problems
type: Item
instance of: scholarly article
title: On resonant Neumann problems
zbMATH Open document ID: 1271.35036
author: Nikolaos S. Papageorgiou
author: Dumitru Motreanu
author: V. V. Motreanu
published in: Mathematische Annalen
publication date: 2013-02-04T00:00:00Z
review text: The authors consider semilinear Neumann elliptic problems, defined on a bounded domain with a smooth boundary. By combining minimax methods based on the critical point theory with techniques from the Morse Theory, they prove the existence of a nontrivial solution for resonant problems with respect to any eigenvalue of the negative Neumann Laplacian, and they present multiplicity results for resonant problems to the first two eigenvalues.
reviewed by: Mohammed Bouchekif
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 6134319
zbMATH Keywords: resonant Neumann problems
zbMATH Keywords: critical point theory
zbMATH Keywords: Morse theory
zbMATH Keywords: existence and multiplicity results
MaRDI profile type: Publication
full work available at URL: s00208-011-0763-z
OpenAlex ID: W2059981650
cites work: Saddle points and multiple solutions of differential equations
cites work: Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
cites work: Q3140494
cites work: Critical point theory and the number of solutions of a nonlinear Dirichlet problem
cites work: Infinite dimensional Morse theory and multiple solution problems
cites work: Q3873183
cites work: SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
cites work: On the antimaximum principle for the \(p\)-Laplacian with indefinite weight
cites work: Nonlinear boundary value problems at resonance
cites work: Nonlinear Two Point Boundary Value Problems at Resonance Without Landesman-Lazer Condition
cites work: On the solvability of a nonlinear second-order elliptic equation at resonance
cites work: Q5588800
cites work: Multiple solutions for semilinear elliptic boundary value problems with double resonance
cites work: Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist
cites work: Remarks on multiple solutions for elliptic resonant problems
cites work: Q3791764
cites work: Variational methods and semilinear elliptic equations
cites work: Critical point theory and Hamiltonian systems
cites work: Multiple existence results of solutions for the Neumann problems via super- and sub-solutions
cites work: Nonlinear Neumann problems near resonance
cites work: Existence and multiplicity of solutions for Neumann problems
cites work: Q5504092
cites work: On a Class of Functionals Invariant under a Z n Action
cites work: Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues
cites work: Solvability of Neumann problem for elliptic equations at resonance
cites work: Existence and multiplicity for solutions of Neumann problem for semilinear elliptic equations.
DOI: 10.1007/S00208-011-0763-Z
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description: scientific article; zbMATH DE number 6134319