On an elliptic equation of Kirchhoff type problem via topological degree

Said Ait Temghart; Abderrazak Kassidi; Chakir Allalou; Adil Abbassi

Said Ait Temghart Laboratory LMACS, FST of Beni Mellal, Sultan Moulay Slimane University, Morocco
Abderrazak Kassidi
Chakir Allalou Laboratory LMACS, FST of Beni Mellal, Sultan Moulay Slimane University,
Adil Abbassi

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.