A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential

Michael Filippakis; Leszek Gasiński; Nikolaos S. Papageorgiou

doi:10.1016/j.na.2004.11.012

A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential

Michael Filippakis, Leszek Gasiński, Nikolaos S. Papageorgiou

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

9 Citations (Scopus)

Abstract

We study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of (-Δ,H01(Z)). Our approach is variational and is based on the nonsmooth critical point theory for locally Lipschitz functions. We prove the existence of at least two nontrivial solutions.

Original language	English
Pages (from-to)	61-75
Number of pages	15
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	61
Issue number	1-2
DOIs	https://doi.org/10.1016/j.na.2004.11.012
Publication status	Published - 15 Apr 2005
Externally published	Yes

Keywords

Eigenvalues and eigenspaces of the Laplacian
Hemivariational inequalities
Local linking
Locally Lipschitz function
Multiple nontrivial critical points
Resonance
Subdifferential
Variational characterizations of the eigenvalues

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10.1016/j.na.2004.11.012

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title = "A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential",

abstract = "We study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of (-Δ,H01(Z)). Our approach is variational and is based on the nonsmooth critical point theory for locally Lipschitz functions. We prove the existence of at least two nontrivial solutions.",

keywords = "Eigenvalues and eigenspaces of the Laplacian, Hemivariational inequalities, Local linking, Locally Lipschitz function, Multiple nontrivial critical points, Resonance, Subdifferential, Variational characterizations of the eigenvalues",

author = "Michael Filippakis and Leszek Gasi{\'n}ski and Papageorgiou, \{Nikolaos S.\}",

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AU - Filippakis, Michael

AU - Gasiński, Leszek

AU - Papageorgiou, Nikolaos S.

PY - 2005/4/15

Y1 - 2005/4/15

N2 - We study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of (-Δ,H01(Z)). Our approach is variational and is based on the nonsmooth critical point theory for locally Lipschitz functions. We prove the existence of at least two nontrivial solutions.

AB - We study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of (-Δ,H01(Z)). Our approach is variational and is based on the nonsmooth critical point theory for locally Lipschitz functions. We prove the existence of at least two nontrivial solutions.

KW - Eigenvalues and eigenspaces of the Laplacian

KW - Hemivariational inequalities

KW - Local linking

KW - Locally Lipschitz function

KW - Multiple nontrivial critical points

KW - Resonance

KW - Subdifferential

KW - Variational characterizations of the eigenvalues

UR - https://www.scopus.com/pages/publications/14544278824

U2 - 10.1016/j.na.2004.11.012

DO - 10.1016/j.na.2004.11.012

M3 - Article

SN - 0362-546X

VL - 61

SP - 61

EP - 75

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 1-2

ER -

A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential

Abstract

Keywords

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