Existence and Uniqueness of Positive Solutions to Three Coupled Nonlinear Schrdinger Equations  

作　　者：Guo-bei FANG Zhong-xue L 

机构地区：[1]School of Mathematics and Statistics,Jiangsu Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2015年第4期1021-1032,共12页应用数学学报（英文版）

基　　金：Supported by the Natural Science Foundation of China(No.10771181,11071206,11271166);NSF of Jiangsu Province(No.BK2010172);sponsored by Qing Lan Project

摘　　要：In this paper, we consider existence and uniqueness of positive solutions to three coupled nonlinear SchrSdinger equations which appear in nonlinear optics. We use the behaviors of minimizing sequences for a bound to obtain the existence of positive solutions for three coupled system. To prove the uniqueness of positive solutions, we use the radial symmetry of positive solutions to transform the system into an ordinary differential system, and then integrate the system. In particular, for N = 1, we prove the uniqueness of positive solutions when 0≤ β=μ1 = μ2 =μ3 or β 〉 max{l,μ2,μ3}.In this paper, we consider existence and uniqueness of positive solutions to three coupled nonlinear SchrSdinger equations which appear in nonlinear optics. We use the behaviors of minimizing sequences for a bound to obtain the existence of positive solutions for three coupled system. To prove the uniqueness of positive solutions, we use the radial symmetry of positive solutions to transform the system into an ordinary differential system, and then integrate the system. In particular, for N = 1, we prove the uniqueness of positive solutions when 0≤ β=μ1 = μ2 =μ3 or β 〉 max{l,μ2,μ3}.

关 键 词：coupled nonlinear SchrSdinger equations positive solution EXISTENCE uniqueness. 

分 类 号：O175.29[理学—数学] O175.2[理学—基础数学]