Existence, Asymptotic Behavior and Uniqueness for Large Solutions to Δu = e q(x)u
Jorge García-Melián, José C. Sabina de Lis, Julio Daniel Rossi · Advanced Nonlinear Studies · 2009
Abstract In this paper we consider existence, asymptotic behavior near the boundary and uniqueness for solutions to Δu = e q(x)u in a bounded smooth domain Ω with the boundary condition u(x) → + ∞ as dist(x, ∂Ω) → 0. The exponent q(x) is assumed to be a Hölder continuous function which is either positive on ∂Ω or is positive in a neighborhood of ∂Ω maybe vanishing on ∂Ω. When dealing with nonnegative exponents q we are allowing nonempty interior regions Ω 0 ⊂ Ω where q vanishes. Changing sign exponents q will be also considered.