A multiplicity theorem for p-superlinear p-Laplacian equations using critical groups and morse theory

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

doi:10.1007/s00605-010-0201-4

A multiplicity theorem for p-superlinear p-Laplacian equations using critical groups and morse theory

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 study a nonlinear elliptic equation driven by the Dirichlet p-Laplacian and with a Carathéodory nonlinearity. We assume that the nonlinearity exhibits a p-superlinear growth near infinity but need not satisfy the Ambrosetti-Rabinowitz condition. Using truncation techniques, minimax methods and Morse theory, we show that the problem admits at least three nontrivial solutions, two of which have constant sign (one positive, the other negative).

Original language	English
Pages (from-to)	471-491
Number of pages	21
Journal	Monatshefte fur Mathematik
Volume	163
Issue number	4
DOIs	https://doi.org/10.1007/s00605-010-0201-4
Publication status	Published - Aug 2011

Keywords

C-condition
Critical groups
Indefinite Euler function
Morse theory
Mountain pass theorem
p-Superlinear nonlinearity

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10.1007/s00605-010-0201-4

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abstract = "We study a nonlinear elliptic equation driven by the Dirichlet p-Laplacian and with a Carath{\'e}odory nonlinearity. We assume that the nonlinearity exhibits a p-superlinear growth near infinity but need not satisfy the Ambrosetti-Rabinowitz condition. Using truncation techniques, minimax methods and Morse theory, we show that the problem admits at least three nontrivial solutions, two of which have constant sign (one positive, the other negative).",

keywords = "C-condition, Critical groups, Indefinite Euler function, Morse theory, Mountain pass theorem, p-Superlinear nonlinearity",

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AU - Papageorgiou, Nikolaos S.

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N2 - We study a nonlinear elliptic equation driven by the Dirichlet p-Laplacian and with a Carathéodory nonlinearity. We assume that the nonlinearity exhibits a p-superlinear growth near infinity but need not satisfy the Ambrosetti-Rabinowitz condition. Using truncation techniques, minimax methods and Morse theory, we show that the problem admits at least three nontrivial solutions, two of which have constant sign (one positive, the other negative).

AB - We study a nonlinear elliptic equation driven by the Dirichlet p-Laplacian and with a Carathéodory nonlinearity. We assume that the nonlinearity exhibits a p-superlinear growth near infinity but need not satisfy the Ambrosetti-Rabinowitz condition. Using truncation techniques, minimax methods and Morse theory, we show that the problem admits at least three nontrivial solutions, two of which have constant sign (one positive, the other negative).

KW - C-condition

KW - Critical groups

KW - Indefinite Euler function

KW - Morse theory

KW - Mountain pass theorem

KW - p-Superlinear nonlinearity

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U2 - 10.1007/s00605-010-0201-4

DO - 10.1007/s00605-010-0201-4

M3 - Article

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SP - 471

EP - 491

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 4

ER -

A multiplicity theorem for p-superlinear p-Laplacian equations using critical groups and morse theory

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Keywords

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