Infinitely many solutions for magnetic fractional problems with critical Sobolev-Hardy nonlinearities

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](2)(s,A))(-Delta)(A)(s)u = lambda f (x, vertical bar u vertical bar)u + vertical bar u vertical bar(2)(*(alpha)-2)(s)u/vertical bar x vertical bar(alpha), in R-N, where s is an element of(0, 1), N > 2s, 2(s)(*)(alpha) = 2(N-alpha)/N-2s is the fractional Hardy-Sobolev critical exponent with alpha is an element of[0, 2s), lambda 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 (-Delta)(A)(s) is 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 lambda.