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arXiv · 1909.04872

Positive solutions for a class of singular Dirichlet problems

Nikolaos S. Papageorgiou·Vicenţiu D. Rădulescu·Dušan D. Repovš
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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 $\lambda>0$ and it need not satisfy the AR-condition. Having as our starting point the work of Diaz-Morel-Oswald (1987), 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.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2019-09-11. Positive solutions for a class of singular Dirichlet problems. https://doi.org/10.1016/j.jde.2019.07.018

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