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On the uniqueness and structure of solutions to a coupled elliptic system |
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| Authors: | Zhi-You Chen Junping Shi Yong-Li Tang |
| Institution: | a Department of Mathematics, National Central University, Chung-Li 32001, Taiwan b Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA c Y.Y. Tseng Functional Analysis Research Center, School of Mathematics, Harbin Normal University, Harbin, Heilongjiang 150080, PR China |
| Abstract: | 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 Schrödinger 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. |
| Keywords: | 35J60 |
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