Positive solutions for a quasilinear elliptic equation of Kirchhoff type

Abstract

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type − M ( ∫ Ω | ∇ u | 2 d x ) Δ u = f ( x , u ) , in Ω , u = 0 , on ∂Ω , where Ω is a smooth bounded domain of ℝ N , M is a positive function, and f has subcritical growth.