A nonlocal sixth order parabolic problem with nonlinear source

Abstract

The purpose of this article is to study the existence of weak solutions for a class of nonlinear nonlocal Dirichlet parabolic problem involving the p(x)-Kirchhoff type triharmonic operator with a nonlinear source. We apply degree theory to operators of the type T + S + C, where T is maximal monotone, S is bounded pseudomonotone, and C is compact with D(T) ⊆ D(C) and satisfies a sublinearity condition, to establish our result within the context of Sobolev spaces with variable exponents.