The existence of two nontrivial solutions via homological local linking for the non-coercive p-Laplacian Neumann problem

Donal O'Regan

doi:10.1016/j.na.2008.10.021

The existence of two nontrivial solutions via homological local linking for the non-coercive p-Laplacian Neumann problem

Donal O'Regan

Mathematics

National Technical University of Athens (NTUA)

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1 Citation (Scopus)

Abstract

In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian and with a Caratheodory right hand side nonlinearity f(z, x). The hypothesis on f(z. x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions. (C) 2008 Elsevier Ltd, All rights reserved.

Original language	English (Ireland)
Pages (from-to)	4386-4392
Number of pages	7
Journal	Nonlinear Analysis-Theory Methods & Applications
Volume	70
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2008.10.021
Publication status	Published - 1 Jun 2009

Keywords

C-condition
Critical groups
Noncoercive Euler functional
PS-condition
p-Laplacian

Authors (Note for portal: view the doc link for the full list of authors)

Authors
O'Regan, D,Papageorgiou, NS

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10.1016/j.na.2008.10.021

Cite this

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abstract = "In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian and with a Caratheodory right hand side nonlinearity f(z, x). The hypothesis on f(z. x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions. (C) 2008 Elsevier Ltd, All rights reserved.",

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N2 - In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian and with a Caratheodory right hand side nonlinearity f(z, x). The hypothesis on f(z. x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions. (C) 2008 Elsevier Ltd, All rights reserved.

AB - In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian and with a Caratheodory right hand side nonlinearity f(z, x). The hypothesis on f(z. x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions. (C) 2008 Elsevier Ltd, All rights reserved.

KW - C-condition

KW - Critical groups

KW - Noncoercive Euler functional

KW - PS-condition

KW - p-Laplacian

UR - https://www.scopus.com/pages/publications/63449093081

U2 - 10.1016/j.na.2008.10.021

DO - 10.1016/j.na.2008.10.021

M3 - Article

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SP - 4386

EP - 4392

JO - Nonlinear Analysis-Theory Methods & Applications

JF - Nonlinear Analysis-Theory Methods & Applications

IS - 12

ER -

The existence of two nontrivial solutions via homological local linking for the non-coercive p-Laplacian Neumann problem

Abstract

Keywords

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