Normalized solutions for nonlinear Schrodinger systems with linear couples

In this paper, we study the normalized solutions to the following system {-Delta u + (V-1(x) +lambda(1)) u = mu(1)vertical bar u vertical bar p(-2)u + beta v in R-N, -Delta v + (V-2(x) +lambda(2)) v = mu(2)vertical bar v vertical bar q(-2)v + beta u in R-N, integral(RN) u(2) - a, integral(RN) v(2) - b, with the mass-subcritical condition 2 < p, q < 2 + 4/N, where mu(1), mu(2), a, b > 0, beta is an element of R \{0} are prescribed; lambda(1), lambda(2) is an element of R are to be determined. We prove the existence of a solution with prescribed L-2-norm under some various conditions on the potential V-1, V-2: R-N -> R. The proof is based on the refined energy estimates. (C) 2021 Elsevier Inc. All rights reserved.