Group-invariant multiple solutions for quasilinear elliptic problems on strip-like domains

In the present paper we prove a multiplicity result for a model quasilinear Neumann problem (Nλ)(Nλ) on strip-like domains, depending on a positive parameter λλ. By variational methods, we prove that for large values of λλ, problem (Nλ)(Nλ) has at least two non-zero weak solutions, while there exists at least a λ˜>0 such that problem (Nλ˜) has at least three non-zero weak solutions. These solutions show symmetry properties with respect to certain group actions.