Positive solutions for nonlinear nonhomogeneous parametric Robin problems

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

We study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Carathéodory reaction term. We prove a bifurcation-type theorem for small values of the parameter. Also, we show that as the parameter ▫$\lambda > 0$▫ approaches zero, we can find positive solutions with arbitrarily big and arbitrarily small Sobolev norm. Finally, we show that for every admissible parameter value, there is a smallest positive solution ▫$u^\ast_\lambda$▫ of the problem, and we investigate the properties of the map ▫$\lambda \mapsto u^\ast_\lambda$▫.

• Jezik: Angleški jezik
• Ključne besede: Robin boundary condition, nonlinear nonhomogeneous differential operator, nonlinear regularity, nonlinear maximum principle, bifurcation-type result, extremal 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: 2018
• Št. strani: Str. 553-580
• Številčenje: Vol. 30, iss. 3
• PID: 20.500.12556/RUL-109200
• UDK: 517.956.2
• ISSN pri članku: 0933-7741
• DOI: 10.1515/forum-2017-0124
• COBISS.SI-ID: 18103641
• Datum objave v RUL: 26.08.2019

Gradivo je del revije

• Naslov: Forum mathematicum
• Skrajšan naslov: Forum math.
• Založnik: de Gruyter
• ISSN: 0933-7741
• COBISS.SI-ID: 26801408