Nontrivial Solutions for a Class ofp-Kirchhoff Dirichlet Problem

Abstract

This paper is devoted to the followingp-Kirchhoff type of problems−a+b∫Ω∇updxΔpu=fx,u,x∈Ωu=0,x∈∂Ωwith the Dirichlet boundary value. We show that thep-Kirchhoff type of problems has at least a nontrivial weak solution. The main tools are variational method, critical point theory, and mountain-pass theorem.