Existence and Non-existence Results for a Quasilinear Problem with Nonlinear Boundary Condition

Abstract

We study the problem-divax|∇u|p-2∇u=λ1+|x|α1|u|q-2u-hx|u|r-2uin Ω⊂RN,ax|∇u|p-2∇u·n+bx·|u|p-2u=θgx,uon Γ,u≥0in Ω,where Ω is an unbounded domain with smooth boundary Γ, n denotes the unit outward normal vector on Γ, and λ0, θ are real parameters. We assume throughout that p