Positive solutions for a class of singular Dirichlet problemsPapageorgiou, Nikolaos S. (Avtor) Rǎdulescu, Vicenţiu (Avtor) Repovš, Dušan (Avtor) singular termsuperlinear perturbationweak comparisonorder coneWe 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) [J.I. Diaz, J.M. Morel, L. Oswald, An elliptic equation with singular nonlinearity, Commun. Partial Differ. Equ. 12 (1987) 1333-1344], we show that there is a critical parameter value ▫$\lambda_\ast$▫ such that for all ▫$\lambda > \lambda_\ast$▫ the problem has two positive solutions, while for ▫$\lambda < \lambda_\ast$▫ there are no positive solutions. What happens in the critical case ▫$\lambda = \lambda_\ast$▫ is an interesting open problem.20192019-09-16 12:30:08Članek v reviji110524sl