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

Abstract

We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a superlinear (convex) term. The superlinearity is not expressed via the Ambrosetti-Rabinowitz condition. Instead, a more general hypothesis is used. We prove a bifurcation-type theorem describing the set of positive solutions as the parameter ▫$\lambda > 0$▫ varies. We also show the existence of a minimal positive solution ▫$\tilde{u}_\lambda$▫ and determine the monotonicity and continuity properties of the map ▫$\lambda \mapsto \tilde{u}_\lambda$▫.

Keywords

indefinite potential;Robin boundary condition;strong maximum principle;truncation;competing nonlinear;positive solutions;regularity theory;minimal positive solution;

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: 18010713 Link will open in a new window
ISSN: 1534-0392
Views: 524
Downloads: 389
Average score: 0 (0 votes)
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Other data

Type (COBISS): Article
Pages: str. 1293-1314
Volume: ǂVol. ǂ16
Issue: ǂno. ǂ4
Chronology: 2017
DOI: 10.3934/cpaa.2017063
ID: 11222018