Periodic problems with the scalar p-Laplacian resonant at any eigenvalue via critical point methods

Sophia Th Kyritsi; Donal O'Regan; Nikolaos S. Papageorgiou

doi:10.1515/ans-2013-0309

Periodic problems with the scalar p-Laplacian resonant at any eigenvalue via critical point methods

Sophia Th Kyritsi
, Donal O'Regan
, Nikolaos S. Papageorgiou

Mathematics

Hellenic Naval Academy
National Technical University of Athens (NTUA)

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

Abstract

We consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carathéodory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.

Original language	English
Pages (from-to)	751-772
Number of pages	22
Journal	Advanced Nonlinear Studies
Volume	13
Issue number	3
DOIs	https://doi.org/10.1515/ans-2013-0309
Publication status	Published - 2013

Keywords

Critical groups
Homotopy equivalence
Linking sets
P-Laplacian
Resonance

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title = "Periodic problems with the scalar p-Laplacian resonant at any eigenvalue via critical point methods",

abstract = "We consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carath{\'e}odory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.",

keywords = "Critical groups, Homotopy equivalence, Linking sets, P-Laplacian, Resonance",

author = "Kyritsi, \{Sophia Th\} and Donal O'Regan and Papageorgiou, \{Nikolaos S.\}",

year = "2013",

doi = "10.1515/ans-2013-0309",

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AU - Kyritsi, Sophia Th

AU - O'Regan, Donal

AU - Papageorgiou, Nikolaos S.

PY - 2013

Y1 - 2013

N2 - We consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carathéodory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.

AB - We consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carathéodory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.

KW - Critical groups

KW - Homotopy equivalence

KW - Linking sets

KW - P-Laplacian

KW - Resonance

UR - https://www.scopus.com/pages/publications/84884402638

U2 - 10.1515/ans-2013-0309

DO - 10.1515/ans-2013-0309

M3 - Article

SN - 1536-1365

VL - 13

SP - 751

EP - 772

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

IS - 3

ER -

Periodic problems with the scalar p-Laplacian resonant at any eigenvalue via critical point methods

Abstract

Keywords

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