Multiplicity of localized solutions of nonlinear Schrodinger systems for infinite attractive case

In this paper, we consider the following nonlinear Schrodinger system: {- epsilon(2)Delta u + V-1(x)u = uv(2) in R-N, u is an element of H-1 (R-N), - epsilon(2)Delta v + V-2(x)v = u(2)v in R-N, v is an element of H-1 (R-N), where N <= 3, epsilon is an element of (0, 1), V-i is an element of C-1 (R-N, R), 0 < inf(x is an element of RN) V-i(x) <= sup(x is an element of RN) V-i(x) < infinity (i = 1,2), and there exists a bounded open set A C RN with smooth boundary partial derivative Lambda such that inf(x is an element of partial derivative Lambda) min {partial derivative V-1/partial derivative nu (x), partial derivative V-2/partial derivative nu (x)} > 0. We prove the existence of a given number of semi-positive solutions localized in Lambda. Here we say (u, v) is semi-positive, if either u > 0 or v > 0. (C) 2020 Elsevier Inc. All rights reserved.