Multiplicity results for a class of asymptotically p-linear equations on ℝN

Abstract

The aim of this paper is investigating the multiplicity of weak solutions of the quasilinear elliptic equation [Formula: see text] in [Formula: see text], where [Formula: see text], the nonlinearity [Formula: see text] behaves as [Formula: see text] at infinity and [Formula: see text] is a potential satisfying suitable assumptions so that an embedding theorem for weighted Sobolev spaces holds. Both the non-resonant and resonant cases are analyzed.