High Perturbations of a Fractional Kirchhoff Equation with Critical Nonlinearities

This paper concerns a fractional Kirchhoff equation with critical nonlinearities and a negative nonlocal term. In the case of high perturbations (large values of α, i.e., the parameter of a subcritical nonlinearity), existence results are obtained by the concentration compactness principle together...

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Bibliographic Details
Published inAxioms Vol. 13; no. 5; p. 337
Main Authors Yu, Shengbin, Huang, Lingmei, Chen, Jiangbin
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.05.2024
Subjects
Asymptotic properties
concentration compactness principle
critical exponent
fractional Kirchhoff equation
Mathematical research
mountain pass theorem
multiplicity
Nonlinear theories
Nonlinearity
Perturbation
Perturbation (Mathematics)
Phase transitions
Theorems
China
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Summary:This paper concerns a fractional Kirchhoff equation with critical nonlinearities and a negative nonlocal term. In the case of high perturbations (large values of α, i.e., the parameter of a subcritical nonlinearity), existence results are obtained by the concentration compactness principle together with the mountain pass theorem and cut-off technique. The multiplicity of solutions are further considered with the help of the symmetric mountain pass theorem. Moreover, the nonexistence and asymptotic behavior of positive solutions are also investigated.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13050337