Positive ground state solutions for a class of fractional coupled Choquard systems

In this paper, we combine the critical point theory and variational method to investigate the following a class of coupled fractional systems of Choquard type [Graphics] with s is an element of (0; 1); N >= 3; alpha is an element of (0; N); p > 1, lambda(i) > 0 are constants for i = 1; 2, beta > 0 is a parameter, and I-alpha(x) is the Riesz Potential. We prove the existence and asymptotic behaviour of positive ground state solutions of the systems by using constrained minimization method and Hardy-Littlewood-Sobolev inequality. Moreover, nonexistence of nontrivial solutions is also obtained.