Existence and multiplicity of solutions for double-phase Robin problems

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

We consider a double phase Robin problem with a Carathéodory nonlinearity. When the reaction is superlinear but without satisfying the Ambrosetti-Rabinowitz condition, we prove an existence theorem. When the reaction is resonant, we prove a multiplicity theorem. Our approach is Morse theoretic, using the notion of homological local linking.

• Language: English
• Keywords: double phase Robin problem, Carathéodory nonlinearity, existence theorem, superlinear case, positive solutions, resonant case
• Work type: Article (dk_c)
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 546-560
• Numbering: Vol. 52, iss. 3
• UDC: 517.956
• ISSN on article: 0024-6093
• DOI: 10.1112/blms.12347
• COBISS.SI-ID: 16036355
• Publication date in RUL: 03.06.2020

Record is a part of a journal

• Title: Bulletin of the London Mathematical Society
• Shortened title: Bull. Lond. Math. Soc.
• Publisher: C.F.Hodgson and Son
• ISSN: 0024-6093
• COBISS.SI-ID: 25154560