On the uniqueness and structure of solutions to a coupled elliptic system
Journal of Differential Equations
In this paper, we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear Schrodinger equation. We establish the existence and uniqueness of solutions to the Dirichlet problem on the ball. In addition, the nonexistence of the ground state solutions under certain conditions on the nonlinearities and the complete structure of different types of solutions to the shooting problem are proved. (C) 2010 Elsevier Inc. All rights reserved.
Chen, Zhi-You; Chern, Jann-Long; Tang, Yong-Li; and Shi, Junping, On the uniqueness and structure of solutions to a coupled elliptic system (2010). Journal of Differential Equations, 249(12), 3419-3442.