On a nonlocal problem involving the generalized anisotropic p(⋅)-Laplace operator

Abstract

In this paper, we study an anisotropic nonlocal problem which is a stationary counterpart of the Kirchhoff equation settled in the variable exponent Sobolev spaces W₀^{1,p(⋅)}(Ω). By using the variational approach and applying the Mountain-Pass theorem along with the Fountain theorem, we obtain the existence and multiplicity of nontrivial weak solutions.