Multiple solutions for a class of N-Kirchhoff type equations via variational methods

In this article, we consider the following N -Kirchhoff type problem - M ∫ Ω | ∇ u | N d x Δ N u = λ f ( x , u ) + μ g ( x , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded smooth domain of R N , N ≥ 2 , M : R 0 + → R is a continuous function, Δ N u = div ( | ∇ u | N - 2 ∇ u ) , f , g : Ω × R → R are two Carathéodory functions and λ , μ are positive parameters. Using variational method, we show the existence of at least three weak solutions for the problem.