Eigenvalues for anisotropic p-Laplacian under a Steklov-like boundary condition

"The eigenvalue problem -div~(1/p∇_ξ (Fᵖ (∇ u))=λ a(x) u q-2u, with q∈ (1, ∞),~ p∈ (Nq/N+q-1, ∞),~ p≠ q, subject to Steklov-like boundary condition, Fᵖ⁻¹(∇ u)∇ _ξ F (∇ u)· ν=λ b(x) u q-2u is investigated on a bounded Lipschitz domain Ω⊂ R^ N,~N≥ 2. Here, F stands for a C²(RN \0\) norm and a∈ L∞(Ω),~ b∈ L∞(∂Ω) are given nonnegative functions satisfying \[ ∫_Ω a~dx+∫∂Ω b~dσ >0. \] Using appropriate variational methods, we are able to prove that the set of eigenvalues of this problem is the interval [0, ∞)."