LEAST ACTION NODAL SOLUTIONS FOR THE QUADRATIC CHOQUARD EQUATION

We prove the existence of a minimal action nodal solution for the quadratic Choquard equation -Delta u + u = (I-alpha * parallel to u parallel to(2))u in R-N, where I-alpha is the Riesz potential of order alpha is an element of (0, N). The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations -Delta u + u = (I-alpha * parallel to u parallel to(p))vertical bar u vertical bar(p-2) u in R-N, when p -> 2. The existence of minimal action nodal solutions for p > 2 can be proved using a variational minimax procedure over a Nehari nodal set. No minimal action nodal solutions exist when p < 2.