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Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces

Stancut I. L., Stircu I. D.

Opuscula Mathematica

2016

Vol. 36, no. 1

81--101

In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential Von a bounded domain in Rn (N ≥ 3) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any λ > 0 is an eigenvalue of our problem. The second theorem states the existence of a constant [formula] such that any [formula] is an eigenvalue, while the third theorem claims the existence of a constant λ* > 0 such that every λ ∈ [λ*∞) is an eigenvalue of the problem.