Existence of solution for a class of nonvariational Kirchhoff type problem via dynamical methods

Abstract

In this paper, we use dynamical methods to establish the existence of nontrivial solution for the following class of Kirchhoff type problem (P)−1+b∫Ω|∇u|2dxΔu=f(u)+h(u,∇u),x∈Ω,u=0,x∈∂Ω, where Ω⊂RN(N=2,3) is a smooth bounded domain, b≥0, f:R→R and h:R×RN→[0,+∞) are C1-functions that satisfy some technical conditions.