EIGENVALUE PROBLEMS FOR ANISOTROPIC EQUATIONS INVOLVING A POTENTIAL ON ORLICZ-SOBOLEV TYPE SPACES

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 lambda > 0 is an eigenvalue of our problem. The second theorem states the existence of a constant lambda(*) > 0 such that any lambda is an element of (0, lambda(*)] is an eigenvalue, while the third theorem claims the existence of a constant lambda* > 0 such that every lambda is an element of [lambda*, infinity) is an eigenvalue of the problem.