Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional -Laplacian operator in ℝ . By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 5; no. 1; pp. 27 - 55
Main Authors Pucci, Patrizia, Xiang, Mingqi, Zhang, Binlin
Format Journal Article
LanguageEnglish
Published De Gruyter 01.02.2016
Subjects
35A15
35J60
35R11
47G20
Fractional
fractional p-laplacian
Kirchhoff type equations
Laplacian
multiple solutions
variational methods
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Summary:The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional -Laplacian operator in ℝ . By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter λ and under suitable general integrability properties of the ratio between some powers of the weights. Finally, existence of infinitely many pair of entire solutions is obtained by genus theory. Last but not least, the paper covers a main feature of Kirchhoff problems which is the fact that the Kirchhoff function can be zero at zero. The results of this paper are new even for the standard stationary Kirchhoff equation involving the Laplace operator.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2015-0102