Three solutions for a perturbed Dirichlet boundary value problem involving the [formula omitted]-Laplacian

Abstract

In this paper, we study the perturbed Dirichlet problem { − Δ p u + a ( x ) | u | p − 2 u = f ( x , u ) + λ g ( x , u ) in Ω , u = 0 on ∂ Ω . Some existence results of three solutions are obtained by using a three critical points Theorem proved by G. Bonanno (2003) [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Anal. 54 (2003) 651–665.].