On fractional Schrodinger systems of Choquard type

In this article, we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schrbdinger-Choquard equation i partial derivative(t)Psi + (-Delta)(alpha) Psi = a vertical bar Psi vertical bar(s-2) psi + lambda(1/vertical bar x vertical bar(N-beta) star vertical bar psi vertical bar(p)) vertical bar Psi vertical bar(p-2) psi in RN+1, where N >= 2 , alpha is an element of (0,1), beta is an element of (0, N), s is an element of (2, 2 + 4 alpha/N), p is an element of [2, 1 + 2 alpha+beta/N), and the constants a, lambda are nonnegative satisfying a + lambda not equal 0. We then extend the arguments to establish similar results for coupled standing waves of nonlinear fractional Schrodinger systems of Choquard type. The same argument works for equations with an arbitrary number of combined nonlinearities and when vertical bar x vertical bar(beta-N) is replaced by a more general convolution potential kappa : R-N -> [0, infinity) under certain assumptions. (C) 2017 Elsevier Inc. All rights reserved.