Existence and multiplicity results for a class of Kirchho type problems involving the p(x)-biharmonic operator

Omar Darhouche

doi:10.5269/bspm.v37i2.32100

Existence and multiplicity results for a class of Kirchho type problems involving the p(x)-biharmonic operator

Omar Darhouche University Mohamed I Department of Mathematics http://orcid.org/0000-0003-2604-1700

DOI: https://doi.org/10.5269/bspm.v37i2.32100

Keywords: Variational method, Mountain pass theorem, p(x)-Biharmonic Operator, Kirchho type equation, Nonlocal problem, Navier boundary conditions, generalized Lebesgue-Sobolev spaces

Abstract

The aim of this paper is to establish the existence and multiplicity of solutions for a class of nonlocal problem involving the p(x)-biharmonic operator. Our technical approach is based on direct variational method and the theory of variable exponent Sobolev spaces.