Existence of weak solution for p-Kirchoff type problem via topological degree

In the present paper, we use the topological degree methods of Berkovits to prove the existence of weak solutions of the following p -Kirchhoff type problems with Dirichlet boundary condition: - M ∫ Ω A ( x , ∇ u ) + 1 p | ∇ u | p d x div a ( x , ∇ u ) - | ∇ u | p - 2 ∇ u = λ H ( x , u , ∇ u ) in Ω , where Ω is a smooth bounded domain of R N , M is a positive function and H , a are the Carathéodory’s functions that satisfy some assumptions.