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- Title
Nontrivial solutions of superlinear nonlocal problems.
- Authors
Molica Bisci, Giovanni; Repovš, Dušan; Servadei, Raffaella
- Abstract
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.
- Subjects
INTEGRO-differential equations; EXISTENCE theorems; FRACTIONAL calculus; VARIATIONAL approach (Mathematics); DIRICHLET problem
- Publication
Forum Mathematicum, 2016, Vol 28, Issue 6, p1095
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2015-0204