Positive solutions for a class of singular Dirichlet problems

Abstract

We consider a Dirichlet elliptic problem driven by the Laplacian with singular and superlinear nonlinearities. The singular term appears on the left-hand side while the superlinear perturbation is parametric with parameter λ>0 and it need not satisfy the AR-condition. Having as our starting point the work of Diaz-Morel-Oswald (1987) [3], we show that there is a critical parameter value λ⁎ such that for all λ>λ⁎ the problem has two positive solutions, while for λ<λ⁎ there are no positive solutions. What happens in the critical case λ=λ⁎ is an interesting open problem.