Nontrivial solutions of superlinear nonlocal problems

Molica Bisci, Giovanni (author), Repovš, Dušan (author), Servadei, Raffaella (author)

We study the question of the existence of infinitely many weak solutions for nonlocal equations of fractional Laplacian type with homogeneous Dirichlet boundary data, in presence of a superlinear term. Starting from the well-known Ambrosetti-Rabinowitz condition, we consider different growth assumptions on the nonlinearity, all of superlinear type. We obtain three different existence results in this setting by using the Fountain Theorem, which extend some classical results for semilinear Laplacian equations to the nonlocal fractional setting.

• Language: English
• Keywords: fractional Laplacian, nonlocal problems, variational method, Fountain theorem, integrodifferential operator, superlinear nonlinearities
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2016
• Number of pages: Str. 1095-1110
• Numbering: Vol. 28, iss. 6
• PID: 20.500.12556/RUL-111093
• UDC: 517.95
• ISSN on article: 0933-7741
• DOI: 10.1515/forum-2015-0204
• COBISS.SI-ID: 17671001
• Publication date in RUL: 23.09.2019

Record is a part of a journal

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