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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Published inNonlinearity Vol. 28; no. 7; pp. 2247 - 2264
Main Authors Binlin, Zhang, Bisci, Giovanni Molica, Servadei, Raffaella
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.07.2015
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.
Bibliography:London Mathematical Society
NON-100547.R1
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/7/2247