Kirchhoff–Hardy Fractional Problems with Lack of Compactness

This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator and involving a Hardy potential and different critical nonlinearities. In particular, we cover the delicate c...

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Bibliographic Details
Published inAdvanced nonlinear studies Vol. 17; no. 3; pp. 429 - 456
Main Authors Fiscella, Alessio, Pucci, Patrizia
Format Journal Article
LanguageEnglish
Published De Gruyter 01.08.2017
Subjects
35J20
35J60
35R11
35S15
Critical Nonlinearities
Hardy Coefficients
Stationary Kirchhoff–Dirichlet Problems
Variational Methods
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ISSN1536-1365
2169-0375
DOI10.1515/ans-2017-6021

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Summary:This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator and involving a Hardy potential and different critical nonlinearities. In particular, we cover the delicate case, that is, when the Kirchhoff function is zero at zero. To overcome the difficulties due to the lack of compactness as well as the degeneracy of the models, we have to make use of different approaches.
ISSN:1536-1365
2169-0375
DOI:10.1515/ans-2017-6021