Eigenvalues for anisotropic p−Laplacian under a Steklov-like boundary condition - BARBU, Luminița (Studia Universitatis Babeș-Bolyai Mathematica, 2021)
The eigenvalue problem −div (1p∇ξ(Fp(∇u))=λa(x)∣u∣q−2u, with q(1, ∞), p(NqN+q-1, ∞), p eq q, subject to Steklov-like boundary condition, Fp−1(∇u)∇ξF(∇u)⋅ν=λb(x)∣u∣q−2u is investigated on a bounded Lipschitz domain ΩR^ N, N≥ 2. Here, F stands for a C^2(R^N{0}) norm and aL^∞(Ω), bL^∞(Ω) are given nonnegative functions satisfying ∫Ωa dx+∫∂Ωb dσ>0. Using appropriate variational methods, we are able to prove that the set of eigenvalues of this problem is the interval [0, ∞). Mathematics Subject Classification (2010): 35J60, 35J92, 35P30.