Superlinear perturbations of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential

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

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when ▫$\lambda$▫ is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.

• Language: English
• Keywords: superlinear perturbation, regularity theory, maximum principle, constant sign and nodal solutions, critical groups, indefinite potential
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: art. 116 (22 str.)
• Numbering: Vol. 75, iss. 3
• PID: 20.500.12556/RUL-118046
• UDC: 517.956.2
• ISSN on article: 1422-6383
• DOI: 10.1007/s00025-020-01234-z
• COBISS.SI-ID: 22444547
• Publication date in RUL: 17.08.2020

Record is a part of a journal

• Title: Results in mathematics
• Shortened title: Results math.
• Publisher: Springer Nature
• ISSN: 1422-6383
• COBISS.SI-ID: 514963225