Three solutions for a Dirichlet boundary value problem involving the pp-Laplacian

In this paper we prove the existence of at least three weak solutions for the problem {Δpu+λf(x,u)=a(x)|u|p−2uin Ω,u=0on ∂Ω. Our main tool is a recent three critical points Theorem of B. Ricceri [On a three critical points theorem, Arch. Math. (Basel) 75 (2000) 220–226].