Multiplicity results for a class of asymptotically p-linear equations on R^N

The aim of this paper is investigating the multiplicity of weak solutions of the quasilinear elliptic equation [-Delta_p u + V(x)|u|^{p-2}u = g(x, u), quad x inR^N, ] where $1<+infty$, $Delta_p u= { m div}(| abla u|^{p-2} abla u)$, the nonlinearity $g$ behaves as $|u|^{p-2}u$ at infinity and $V$ is a potential satisfying the assumptions in cite{bf}, so that a suitable embedding theorem for weighted Sobolev spaces holds. Both the non--resonant and the resonant case are analyzed.