On a nonlinear differential equation involving the p(x)-triharmonic operator

Abstract

In this paper, we study weak solutions of a class of nonlinear elliptic Navier boundary value problems involving the p(x)-triharmonic operator. We determine the intervals of parameters for which the problem admits either a sequence of weak solutions converging to zero or an unbounded sequence of weak solutions. Keywords. Weak solutions; Three critical points theorem; Navier boundary conditions; p(x)-triharmonic operator. x∈Ω p(x) ≤ p + := sup x∈Ω p(x).