Robin problems with indefinite linear part and competition phenomena

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

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 ▫$\lambda \mapsto \tilde{u}_\lambda$▫.

• Language: English
• Keywords: indefinite potential, Robin boundary condition, strong maximum principle, truncation, competing nonlinear, positive solutions, regularity theory, minimal positive solution
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 1293-1314
• Numbering: Vol. 16, no. 4
• PID: 20.500.12556/RUL-110196
• UDC: 517.956.2
• ISSN on article: 1534-0392
• DOI: 10.3934/cpaa.2017063
• COBISS.SI-ID: 18010713
• Publication date in RUL: 12.09.2019

Record is a part of a journal

• Title: Communications on pure and applied analysis
• Shortened title: Commun. pure appl. anal.
• Publisher: AIMS Press
• ISSN: 1534-0392
• COBISS.SI-ID: 15066457