Infinitely many sign-changing solutions for Choquard equation with doubly critical exponents

In this paper, we consider the following Choquard equation: - Delta u + u = (I-alpha * F(u))F' (u) in R-N where N >= 3, alpha is an element of (0, N), I-alpha is the Riesz potential, and F(u) := 1/p vertical bar u vertical bar(p) + 1/q vertical bar u vertical bar(q), where p = N+alpha/N and q = N+alpha/N-2 are lower and upper critical exponents in sense of the Hardy- Littlewood-Sobolev inequality. Based on perturbation method and the invariant sets of descending flow, we prove that the above equation possesses infinitely many sign-changing solutions. Our results extend the results in Seok [Nonlinear Choquard equations: doubly critical case. Appl Math Lett. 2018;76:148- 156] and Su [New result for nonlinear Choquard equations: doubly critical case. Appl Math Lett. 2020;102(106092):0-7].