Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

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) [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.

Keywords

singular term;superlinear perturbation;weak comparison;order cone;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956.2
COBISS: 18687833 Link will open in a new window
ISSN: 0022-0396
Views: 480
Downloads: 415
Average score: 0 (0 votes)
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Other data

Type (COBISS): Article
Pages: str. 6539-6554
Volume: ǂVol. ǂ267
Issue: ǂiss. ǂ11
Chronology: Nov. 2019
DOI: 10.1016/j.jde.2019.07.018
ID: 11225338