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Infinitely many solutions for magnetic fractional problems with critical Sobolev‐Hardy nonlinearities
Author(s) -
Yang Libo,
An Tianqing
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5317
Subject(s) - mathematics , sobolev space , degenerate energy levels , function (biology) , operator (biology) , mountain pass theorem , mathematical analysis , exponent , fractional calculus , critical exponent , pure mathematics , nonlinear system , physics , geometry , scaling , quantum mechanics , biochemistry , chemistry , linguistics , philosophy , repressor , evolutionary biology , gene , transcription factor , biology
In this paper, we study the existence of infinitely many solutions of the following degenerate magnetic fractional problem involving critical Sobolev‐Hardy nonlinearities: M ( [ u ] s , A 2 ) ( − △ ) A s u = λ f ( x , | u | ) u + | u | 2 s ∗ ( α ) − 2 u | x | α, i nR N , where s ∈ (0,1), N > 2 s ,2 s ∗ ( α ) = 2 ( N − α ) N − 2 sis the fractional Hardy‐Sobolev critical exponent with α ∈ [0,2 s ), λ is a positive real parameter, M : R 0 + → R 0 +is a Kirchhoff function, A : R N → R N is a magnetic potential function, and( − △ ) A sis the fractional magnetic operator. By using the new version of symmetric mountain pass theorem of Kajikiya, we prove that the problem admits infinitely many solutions for the suitable value of λ.