Normalized saddle solutions for a mass supercritical Choquard equation

We investigate the existence of saddle type normalized solutions for the nonlinear Choquard equation: [GRAPHICS] . Here N >=> 1, a > 0 is given in advance, I-alpha is the Riesz potential of order alpha is an element of (0, N) and the unknown parameter lambda appears as a Lagrange multiplier. In a mass supercritical setting on F, we prove the existence of a couple (u(a)(G) , lambda(G)(a)) is an element of H-1(R-N) x R- of saddle solutions for any a > 0 and for given finite Coxeter group G with its rank k <= N. Our method is to combine the concentration compactness principle with a minimax procedure in the saddle type symmetric subspace, which gives a variational framework of constructing normalized saddle solutions for the Choquard equation. (c) 2023 Elsevier Inc. All rights reserved.