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

Zhi You Chen; Jann Long Chern; Junping Shi; Yong Li Tang

doi:10.1016/j.jde.2010.09.001

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

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 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 language	English
Pages (from-to)	3419-3442
Number of pages	24
Journal	Journal of Differential Equations
Volume	249
Issue number	12
DOIs	https://doi.org/10.1016/j.jde.2010.09.001
Publication status	Published - 2010 Dec 15
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2010.09.001

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title = "On the uniqueness and structure of solutions to a coupled elliptic system",

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 Schr{\"o}dinger 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.",

author = "Chen, {Zhi You} and Chern, {Jann Long} and Junping Shi and Tang, {Yong Li}",

year = "2010",

month = dec,

day = "15",

doi = "10.1016/j.jde.2010.09.001",

language = "English",

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journal = "Journal of Differential Equations",

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AU - Chen, Zhi You

AU - Chern, Jann Long

AU - Shi, Junping

AU - Tang, Yong Li

PY - 2010/12/15

Y1 - 2010/12/15

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.

AB - 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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U2 - 10.1016/j.jde.2010.09.001

DO - 10.1016/j.jde.2010.09.001

M3 - Article

AN - SCOPUS:78049255362

SN - 0022-0396

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SP - 3419

EP - 3442

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 12

ER -

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

Abstract

ASJC Scopus subject areas

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