EIGENVALUE PROBLEMS FOR ANISOTROPIC EQUATIONS INVOLVING A POTENTIAL ON ORLICZ-SOBOLEV TYPE SPACES Ionela-Loredana St†ncuµ and Iulia Dorotheea Stîrcu

In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential V on a bounded domain in R N (N 3) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any > 0 is an eigenvalue of our problem. The second theorem states the existence of a constant > 0 such that any 2 (0, ) is an eigenvalue, while the third theorem claims the existence of a constant > 0 such that every 2 ( ,1) is an eigenvalue of the problem.