Uniqueness of positive solutions to some Schrodinger systems

This paper is devoted to the study of the uniqueness of positive solutions of the following coupled Schrodinger equations: { -Delta u + lambda u = mu(1)u(3) + beta v(2)u - gamma v in Omega, -Delta v + lambda v = mu(2)v(3) + beta u(2)v - gamma u in Omega, u > 0, v > 0 in Omega, u = v = 0 on partial derivative Omega (or u,v is an element of H-1 (R-N) AS Omega = R-N), where N <= 3, Omega subset of R-N is a smooth domain lambda, mu(1), mu(2) are positive constants, beta and gamma are nonlinear and linear coupling constants respectively. We prove some new results on the uniqueness of positive solutions in several cases, improving and strengthening earlier works in the literature. (C) 2020 Elsevier Ltd. All rights reserved.