Normalized solutions of linearly coupled Choquard system with potentials

In this paper, we consider the existence of solutions for the linearly coupled Choquard system with potentials {-Delta u+lambda(1)u+V-1(x)u=mu(1)(I-alpha star|u|(p))|u|(p-2)u+beta(x)v, x is an element of R-N, -Delta v+lambda(2)v+V-2(x)v=mu(2)(I alpha star|v|q)|v|q-2v+beta(x)u, under the constraint integral(N)(R)u(2)dx=xi(2),integral(N)(R)v(2)dx=eta(2), where N >= 3,I-alpha=1/|x|(N-alpha),alpha is an element of (0,N),1+alpha/N<p,q<N+alpha/N-2,mu(1)>0,mu(2)>0 and beta(x) is a fixed function.