Existence Results for a Class of p(x)-Kirchhoff Problems.

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Robin boundary data as follows: − M ∫ Ω 1 p (x) ∇ u p (x) d x + ∫ ∂ Ω β (x) p (x) ∇ u p (x) d σ div( ∇ u p(x)-2 ∇ u)=f(x,u)in Ω , ∇ u p (x) − 2 ∂ u ∂ v + β (x) u p (x) − 2 u = 0 on ∂ Ω , Where β ∈ L ∞ (∂ Ω) and f : Ω × ℝ → ℝ satisfies Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions. [ABSTRACT FROM AUTHOR]