Robin problems with indefinite linear part and competition phenomena
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

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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
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Number of pages:str. 1293-1314
Numbering:Vol. 16, no. 4
ISSN on article:1534-0392
DOI:10.3934/cpaa.2017063 This link opens in a new window
COBISS.SI-ID:18010713 This link opens in a new window
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Record is a part of a journal

Title:Communications on pure and applied analysis
Shortened title:Commun. pure appl. anal.
Publisher:AIMS Press
COBISS.SI-ID:15066457 This link opens in a new window

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