On an elliptic equation of Kirchhoff type problem via topological degree

Abstract

In this paper, we establish the existence of solutions for a nonlinear Dirichlet boundary value problem with Kirchhoff term. Our proof is based on a transform this nonlocal elliptic problem into a new one governed by a Hammerstein equation. The conclusion then follows by using the topological degree theory for operators of $(S_+)$ type in the framework of weighted Sobolev spaces.