Positive solutions for nonlinear nonhomogeneous parametric Robin problems

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

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 $\lambda \mapsto u^\ast_\lambda$.

• Language: English
• Keywords: Robin boundary condition, nonlinear nonhomogeneous differential operator, nonlinear regularity, nonlinear maximum principle, bifurcation-type result, extremal positive solution
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2018
• Number of pages: Str. 553-580
• Numbering: Vol. 30, iss. 3
• PID: 20.500.12556/RUL-109200
• UDC: 517.956.2
• ISSN on article: 0933-7741
• DOI: 10.1515/forum-2017-0124
• COBISS.SI-ID: 18103641
• Publication date in RUL: 26.08.2019

PAPAGEORGIOU, Nikolaos S., RǍDULESCU, Vicenţiu and REPOVŠ, Dušan, 2018, Positive solutions for nonlinear nonhomogeneous parametric Robin problems. Forum mathematicum [online]. 2018. Vol. 30, no. 3, p. 553–580. [Accessed 17 April 2025]. DOI 10.1515/forum-2017-0124. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109200

Record is a part of a journal

• Title: Forum mathematicum
• Shortened title: Forum math.
• Publisher: de Gruyter
• ISSN: 0933-7741
• COBISS.SI-ID: 26801408