Existence of Three Solutions for a Boundary Value Problem in N-dimensional Case

In this paper, the existence of at least three weak solutions for Dirichlet problem where δp_u = div(∣∇u∣^p−2∇u) is the p-Laplacian operator, Ω ⊂ R^N(N ≥ 1) is non-empty bounded open set with smooth boundary ∂Ω, p > N, λ ≥ 0, f: R → R is a continuous function and positive weight function is established. The approach is based on variational methods and critical points.