On a class of two-dimensional singular elliptic problems
Paolo Caldiroli, Roberta Musina · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2001
We consider Dirichlet problems of the form −| x | α Δ u = 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.