Superlinear nonlocal fractional problems with infinitely many solutions

In this paper we study the existence of infinitely many weak solutions for equations driven by nonlocal integrodifferential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian where s ∈ (0, 1) is fixed. We consider different supe...

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Bibliographic Details
Published in:Nonlinearity 2015-07, Vol.28 (7), p.2247-2264
Main Authors: Binlin, Zhang, Bisci, Giovanni Molica, Servadei, Raffaella
Format: Article
Language:English
Subjects:
Boundary conditions
Dirichlet problem
fountain theorem
fractional Laplacian
Mathematical analysis
Mathematical models
Nonlinearity
nonlocal problems
Operators
Texts
Theorems
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Summary:In this paper we study the existence of infinitely many weak solutions for equations driven by nonlocal integrodifferential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian where s ∈ (0, 1) is fixed. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-known Ambrosetti-Rabinowitz condition. In this framework we obtain three different results about the existence of infinitely many weak solutions for the problem under consideration, by using the Fountain Theorem. All these theorems extend some classical results for semilinear Laplacian equations to the nonlocal fractional setting.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/7/2247