Multiple solutions for quasilinear elliptic equations with sign-changing potential

Abstract

In this article, we study the quasilinear elliptic equation -Δpu - (Δpu2)u + V(x)|u|p-2 u = g(x, u), x ∈ ℝN, where the potential V(x) and the nonlinearity g(x, u) are allowed to be sign-changing. Under some suitable assumptions on V and g, we obtain the multiplicity of solutions by using minimax methods.