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We study the boundary value problem −div((|∇u|p 1(x) 2 + |∇u|p 2(x) 2 )∇u) = λ|u|q(x) 2u in , u = 0 on ∂, where is a bounded domain in RN with smooth boundary, λ is a positive real number, and the continuous functions p1, p2, and q satisfy 1 < p2(x) < q(x) < p1(x) < N and maxy2 q(y) < Np 2(x) N p2(x) for any x ∈ . The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that any λ ∈ (λ1, ∞) is an eigenvalue, while any λ ∈ (0, λ0) is not an eigenvalue of the above problem.

Continuous spectrum for a class of nonhomogeneous differential operators