MULTIPLICITY OF SOLUTIONS TO A NONLOCAL CHOQUARD EQUATION INVOLVING FRACTIONAL MAGNETIC OPERATORS AND CRITICAL EXPONENT

In this article, we study the multiplicity of solutions to a nonlocal fractional Choquard equation involving an external magnetic potential and critical exponent, namely, (a + b[u](s,A)(2))(-Delta)(A)(8)u + V(x)u = integral(RN) vertical bar u(y)vertical bar(2u,8*)/vertical bar x - y vertical bar(u)dy vertical bar u vertical bar(2u,8*-2) u + lambda h(n)vertical bar u vertical bar(p-2)u in R-N, [u](s,A) = (integral(RN) integral(RN) vertical bar u(x) - e(i(x - y)center dot A(x+y)/2) u(y)vertical bar(2)/vertical bar x - y vertical bar(N + 28) dx dy)(1/2) where a >= 0, b > 0, 0 < s < min{1, N/4}, 4s <= mu < N, V : R-N -> R is a signchanging scalar potential, A : R-N -> R-N is the magnetic potential, (- Delta)(A)(s) is the fractional magnetic operator, lambda > 0 is a parameter, 2(mu,s)(*) = 2N - mu/N - 2(8) is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality and 2 < p < 2(s)(*). Under suitable assumptions on a, b and lambda, we obtain multiplicity of nontrivial solutions by using variational methods. In particular, we obtain the existence of infinitely many nontrivial solutions for the degenerate Kirchhoff case, that is, a = 0, b > 0.