Multiplicity result for a double eigenvalue quasilinear problem on unbounded domain

In this paper we prove a multiplicity result for a double eigenvalue quasilinear problem on unbounded domain with nonlinear boundary conditions. We use a recent Ricceri-type result of Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Anal. TMA 54 (2003) 651–665]. This result completes some recent results obtained in this direction.