On an elliptic equation of p-Kirchhoff type via variational methods

Abstract

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the p-Kirchhoff type -[M(f Ω|∇u|p dx)]p-1 Δpu = f(x,u) in Ω, u=0 on ∂Ω and -[M(fΩ|∇u| p dx)]p-1 Δpu = f(x,u) +λ|u| s-2in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain of double-struck R signN, 1 < p