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 ...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}.展开更多
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
文摘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}.
