Abstract
In this article, we study the existence of nontrivial solutions for the following p(x) Kirchhoff-type problem
{-M(integral(Omega)A(x, del u) dx) div(a(x, del u))
= lambda h(x)(partial derivative F/partial derivative u)(x, u) in Omega
u = 0, on partial derivative Omega,
where Omega subset of R-n, n >= 3, is a smooth bounded domain, lambda > 0, h is an element of C(Omega), F : Omega x R -> R is continuously differentiable and a, A : Omega x R-n -> R-n are continuous. The proof is based on variational arguments and the theory of variable exponent Sobolev spaces.