Abstract. 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 λ > 0 is an eigenvalue of our problem. The second theorem states the existence of a constant λ * > 0 such that any λ ∈ (0, λ * ] 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.

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