On the uniqueness and structure of solutions to a coupled elliptic system

Zhi-You Chen, Jann Long Chern, Junping Shi, Yong Li Tang

Research output: Contribution to journalArticle

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3419-3442
Number of pages24
JournalJournal of Differential Equations
Volume249
Issue number12
DOIs
Publication statusPublished - 2010 Dec 15

Fingerprint

Ground State Solution
Nonlinear Elliptic Systems
Shooting
Elliptic Systems
Stationary States
Existence and Uniqueness of Solutions
Nonlinear equations
Coupled System
Ground state
Dirichlet Problem
Nonexistence
Nonlinear Equations
Ball
Uniqueness
Nonlinearity

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Chen, Zhi-You ; Chern, Jann Long ; Shi, Junping ; Tang, Yong Li. / On the uniqueness and structure of solutions to a coupled elliptic system. In: Journal of Differential Equations. 2010 ; Vol. 249, No. 12. pp. 3419-3442.
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On the uniqueness and structure of solutions to a coupled elliptic system. / Chen, Zhi-You; Chern, Jann Long; Shi, Junping; Tang, Yong Li.

In: Journal of Differential Equations, Vol. 249, No. 12, 15.12.2010, p. 3419-3442.

Research output: Contribution to journalArticle

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N2 - 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.

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