Uniqueness of positive solutions to some coupled cooperative variational elliptic systems

Yulian An; Jann Long Chern; Junping Shi

doi:10.1090/tran/7207

Uniqueness of positive solutions to some coupled cooperative variational elliptic systems

Yulian An
, Jann Long Chern
, Junping Shi

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

3 Citations (Scopus)

Abstract

The uniqueness of positive solutions to some semilinear elliptic systems with variational structure arising from mathematical physics is proved. The key ingredient of the proof is the oscillatory behavior of solutions to lin-earized equations for cooperative semilinear elliptic systems of two equations on one-dimensional domains, and it is shown that the stability of the positive solutions for such a semilinear system is closely related to the oscillatory behavior.

Original language	English
Pages (from-to)	5209-5243
Number of pages	35
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	7
DOIs	https://doi.org/10.1090/tran/7207
Publication status	Published - 2018 Jul
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/tran/7207

Cite this

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title = "Uniqueness of positive solutions to some coupled cooperative variational elliptic systems",

abstract = "The uniqueness of positive solutions to some semilinear elliptic systems with variational structure arising from mathematical physics is proved. The key ingredient of the proof is the oscillatory behavior of solutions to lin-earized equations for cooperative semilinear elliptic systems of two equations on one-dimensional domains, and it is shown that the stability of the positive solutions for such a semilinear system is closely related to the oscillatory behavior.",

author = "Yulian An and Chern, \{Jann Long\} and Junping Shi",

note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

month = jul,

doi = "10.1090/tran/7207",

language = "English",

volume = "370",

pages = "5209--5243",

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AU - An, Yulian

AU - Chern, Jann Long

AU - Shi, Junping

PY - 2018/7

Y1 - 2018/7

N2 - The uniqueness of positive solutions to some semilinear elliptic systems with variational structure arising from mathematical physics is proved. The key ingredient of the proof is the oscillatory behavior of solutions to lin-earized equations for cooperative semilinear elliptic systems of two equations on one-dimensional domains, and it is shown that the stability of the positive solutions for such a semilinear system is closely related to the oscillatory behavior.

AB - The uniqueness of positive solutions to some semilinear elliptic systems with variational structure arising from mathematical physics is proved. The key ingredient of the proof is the oscillatory behavior of solutions to lin-earized equations for cooperative semilinear elliptic systems of two equations on one-dimensional domains, and it is shown that the stability of the positive solutions for such a semilinear system is closely related to the oscillatory behavior.

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UR - https://www.scopus.com/pages/publications/85045687071#tab=citedBy

U2 - 10.1090/tran/7207

DO - 10.1090/tran/7207

M3 - Article

AN - SCOPUS:85045687071

SN - 0002-9947

VL - 370

SP - 5209

EP - 5243

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

Uniqueness of positive solutions to some coupled cooperative variational elliptic systems

Abstract

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