Parametric nonlinear resonant Robin problems

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

We consider a nonlinear Robin problem driven by the ▫$p$▫-Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly ▫$(p-1)$▫-sublinear and the other one is ▫$(p-1)$▫-linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all big values of the parameter ▫$\lambda$▫ the problem has at least five nontrivial smooth solutions.

• Language: English
• Keywords: indefinite and unbounded potential, critical groups, multiple solutions, nonlinear regularity, resonance, Robin boundary condition, strong comparison, truncation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2019
• Number of pages: Str. 2456-2480
• Numbering: Vol. 292, iss. 11
• PID: 20.500.12556/RUL-113103
• UDC: 517.956.2
• ISSN on article: 0025-584X
• DOI: 10.1002/mana.201800505
• COBISS.SI-ID: 18720857
• Publication date in RUL: 04.12.2019

Record is a part of a journal

• Title: Mathematische Nachrichten
• Shortened title: Math. Nachr.
• Publisher: Wiley
• ISSN: 0025-584X
• COBISS.SI-ID: 25915392