Positive solutions for a class of singular Dirichlet problems

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 lambda > 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 lambda(*) such that for all lambda > lambda(*) the problem has two positive solutions, while for lambda < lambda(*) there are no positive solutions. What happens in the critical case lambda = lambda(*) is an interesting open problem. (C) 2019 Elsevier Inc. All rights reserved.