A morse theoretic approach to the existence of multiple solutions for nonlinear periodic problems

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

A morse theoretic approach to the existence of multiple solutions for nonlinear periodic problems

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 a nonlinear periodic problem driven by the scalar p-Laplacian and with a Carathéodory nonlinearity which asymptotically at infinity exhibits a p-linear growth. Using minimax arguments, together with truncation techniques and methods from Morse theory, we show that the problem has three nontrivial solutions. In the semilinear case (i.e., p=2), we show using Morse theory, that the problem has four nontrivial solutions.

Original language	English
Pages (from-to)	291-318
Number of pages	28
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume	19
Issue number	3
Publication status	Published - 2012

Keywords

Critical groups
Morse theory
Mountain pass theorem
Multiple solutions
Periodic scalar p-Laplacian

Cite this

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abstract = "We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a Carath{\'e}odory nonlinearity which asymptotically at infinity exhibits a p-linear growth. Using minimax arguments, together with truncation techniques and methods from Morse theory, we show that the problem has three nontrivial solutions. In the semilinear case (i.e., p=2), we show using Morse theory, that the problem has four nontrivial solutions.",

keywords = "Critical groups, Morse theory, Mountain pass theorem, Multiple solutions, Periodic scalar p-Laplacian",

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journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis",

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A morse theoretic approach to the existence of multiple solutions for nonlinear periodic problems. / Kyritsi, Sophia Th; O'Regan, Donal; Papageorgiou, Nikolaos S.
In: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, Vol. 19, No. 3, 2012, p. 291-318.

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

TY - JOUR

T1 - A morse theoretic approach to the existence of multiple solutions for nonlinear periodic problems

AU - Kyritsi, Sophia Th

AU - O'Regan, Donal

AU - Papageorgiou, Nikolaos S.

PY - 2012

Y1 - 2012

N2 - We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a Carathéodory nonlinearity which asymptotically at infinity exhibits a p-linear growth. Using minimax arguments, together with truncation techniques and methods from Morse theory, we show that the problem has three nontrivial solutions. In the semilinear case (i.e., p=2), we show using Morse theory, that the problem has four nontrivial solutions.

AB - We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a Carathéodory nonlinearity which asymptotically at infinity exhibits a p-linear growth. Using minimax arguments, together with truncation techniques and methods from Morse theory, we show that the problem has three nontrivial solutions. In the semilinear case (i.e., p=2), we show using Morse theory, that the problem has four nontrivial solutions.

KW - Critical groups

KW - Morse theory

KW - Mountain pass theorem

KW - Multiple solutions

KW - Periodic scalar p-Laplacian

UR - https://www.scopus.com/pages/publications/84861414841

M3 - Article

SN - 1201-3390

VL - 19

SP - 291

EP - 318

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

IS - 3

ER -

A morse theoretic approach to the existence of multiple solutions for nonlinear periodic problems

Abstract

Keywords

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