Saddle solutions for the Choquard equation with a general nonlinearity

In the spirit of Berestycki and Lions (Arch. Rational Mech. Anal., 82: 313-345, 1983), we prove the existence of saddle-type nodal solutions for the Choquard equation -Delta u + u = (I-alpha * F(u))F '(u) in R-N where N >= 2 and I-alpha is the Riesz potential of order alpha is an element of(0, N). Given a finite Coxeter group G with rank k <= N, we construct a G-groundstate uniformly with lowest energy amongst G-saddle solutions for the Choquard equation in a noncompact setting. Moreover, if F ' is odd and has constant sign on (0, +infinity), then every G-groundstate maintains signed on the fundamental domain of the corresponding Coxeter group and receives opposite signs on any two adjacent regions so that nodal domains of G-groundstate are of cone shapes demonstrating Coxeter's symmetric configurations in R-N. These results further complete the variational framework in constructing sign-changing solutions for the Choquard equation but still require a quadratic or super-quadratic growth on F near the origin.