Robin problems with indefinite linear part and competition phenomena

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

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

• Jezik: Angleški jezik
• Ključne besede: indefinite potential, Robin boundary condition, strong maximum principle, truncation, competing nonlinear, positive solutions, regularity theory, minimal positive solution
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2017
• Št. strani: Str. 1293-1314
• Številčenje: Vol. 16, no. 4
• PID: 20.500.12556/RUL-110196
• UDK: 517.956.2
• ISSN pri članku: 1534-0392
• DOI: 10.3934/cpaa.2017063
• COBISS.SI-ID: 18010713
• Datum objave v RUL: 12.09.2019

Gradivo je del revije

• Naslov: Communications on pure and applied analysis
• Skrajšan naslov: Commun. pure appl. anal.
• Založnik: AIMS Press
• ISSN: 1534-0392
• COBISS.SI-ID: 15066457