On a Dirichlet problem involving p-Laplacian
G. A. Afrouzi, Shapour Heidarkhani · International Mathematical Forum · 2007
In this paper, the existence of at least three weak solutions for Dirich-let problem { Δpu + λf(x, u) = 0 in Ω, u = 0 on ∂Ω, where Δpu =div(|∇u|p−2∇u) is the p-Laplacian operator, Ω ⊂ RN (N ≥ 1) is non-empty bounded open set with smooth boundary ∂Ω, p> N, λ> 0 and f: Ω×R → R is a L1-Caratheodory function, is established. The approach is based on variational methods and critical points.