Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator

Mustafa Avci

Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator

Mustafa Avci

Centre for Science

Research output: Contribution to journal › Journal Article › peer-review

21 Citations (Scopus)

Abstract

In this article, we study superlinear Dirichlet problems involving the p(x)-Laplace operator without using the Ambrosetti-Rabinowitz's superquadraticity condition. Using a variant Fountain theorem, but not including Palais-Smale type assumptions, we prove the existence and multiplicity of the solutions.

Original language	English
Journal	Electronic Journal of Differential Equations
Volume	2013
Publication status	Published - 14 Jan. 2013

Keywords

Fountain theorem
P(x)-laplace operator
Variable exponent lebesgue-Sobolev spaces
Variational approach

Cite this

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abstract = "In this article, we study superlinear Dirichlet problems involving the p(x)-Laplace operator without using the Ambrosetti-Rabinowitz's superquadraticity condition. Using a variant Fountain theorem, but not including Palais-Smale type assumptions, we prove the existence and multiplicity of the solutions.",

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T1 - Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator

AU - Avci, Mustafa

PY - 2013/1/14

Y1 - 2013/1/14

N2 - In this article, we study superlinear Dirichlet problems involving the p(x)-Laplace operator without using the Ambrosetti-Rabinowitz's superquadraticity condition. Using a variant Fountain theorem, but not including Palais-Smale type assumptions, we prove the existence and multiplicity of the solutions.

AB - In this article, we study superlinear Dirichlet problems involving the p(x)-Laplace operator without using the Ambrosetti-Rabinowitz's superquadraticity condition. Using a variant Fountain theorem, but not including Palais-Smale type assumptions, we prove the existence and multiplicity of the solutions.

KW - Fountain theorem

KW - P(x)-laplace operator

KW - Variable exponent lebesgue-Sobolev spaces

KW - Variational approach

UR - https://www.scopus.com/pages/publications/84872814691

M3 - Journal Article

AN - SCOPUS:84872814691

VL - 2013

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator

Abstract

Keywords

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