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

Abstract

In this paper, we study the existence of infinitely many solutions of the following degenerate magnetic fractional problem involving critical Sobolev‐Hardy nonlinearities: urn:x-wiley:mma:media:mma5317:mma5317-math-0001 where s ∈ (0,1), N > 2s, is the fractional Hardy‐Sobolev critical exponent with α ∈ [0,2s), λ is a positive real parameter, is a Kirchhoff function, is a magnetic potential function, and 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 λ.