PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS
Abstract
We consider Dirichlet problems of the form
-|x|^α Δu = λu + g(u) in Ω,
u = 0 on ∂Ω,
where α, λ ∈ ℝ, g ∈ C(ℝ) is a superlinear and subcritical function, and Ω is a domain in ℝ^2. We study the existence of positive solutions with respect to the values of the parameters α and λ, and according that 0 ∈ Ω or 0 ∈ ∂Ω, and that Ω is an exterior domain or not.
