IJPAM: Volume 84, No. 5 (2013)

NONLINEAR EIGENVALUE PROBLEM WITHOUT
AMBROSETTI AND RABINOWITZ CONDITION:
AN ORLICZ SPACE SETTING

Nawel Benouhiba1, Hacene Saker2
1,2Department of Mathematics
LMA, Badji Mokhtar-Annaba University
P.O. Box 12 El Hadjar Annaba 23000, ALGERIA


Abstract. We study the Dirichlet boundary value problem for the p(x)-Laplacian of the form
p(x)u=λ f(x,u), x ∈ Ω,
u=0, x ∈ ∂Ω.
We introduce a new variational technic that allows us to investigate problem above without need of the Ambrosetti and Rabinowitz condition on the nonlinearity f.

Received: December 6, 2012

AMS Subject Classification: 35B45, 35J60, 35J70

Key Words and Phrases: p(x)-Laplacian, Variable exponent Lebesgue-Sobolev spaces, eigenvalue, critical point

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DOI: 10.12732/ijpam.v84i5.11 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 5