Existence, uniqueness and stability of positive solutions to sublinear elliptic systems

Jann Long Chern; Yong Li Tang; Chang Shou Lin; Junping Shi

doi:10.1017/S0308210509001115

Existence, uniqueness and stability of positive solutions to sublinear elliptic systems

Jann Long Chern^*
, Yong Li Tang
, Chang Shou Lin
, Junping Shi

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

The existence, stability and uniqueness of positive solutions to a semilinear elliptic system with sublinear nonlinearities are proved. It is shown that the precise global bifurcation diagram of the positive solutions is a monotone curve with different asymptotical behaviour according to the form of the nonlinearities. Equations with Hölder continuous nonlinearities are also considered.

Original language	English
Pages (from-to)	45-64
Number of pages	20
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	141
Issue number	1
DOIs	https://doi.org/10.1017/S0308210509001115
Publication status	Published - 2011 Feb
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Existence, uniqueness and stability of positive solutions to sublinear elliptic systems",

abstract = "The existence, stability and uniqueness of positive solutions to a semilinear elliptic system with sublinear nonlinearities are proved. It is shown that the precise global bifurcation diagram of the positive solutions is a monotone curve with different asymptotical behaviour according to the form of the nonlinearities. Equations with H{\"o}lder continuous nonlinearities are also considered.",

author = "Chern, \{Jann Long\} and Tang, \{Yong Li\} and Lin, \{Chang Shou\} and Junping Shi",

note = "Funding Information: We thank the anonymous referee for helpful suggestions and comments. J.L.C. was partly supported by the National Science Council of Taiwan Grant no. 97-2115-M008-011. J.S. was partly supported by the National Natural Science Foundation of China Grant no. 10671049, the Longjiang Professorship and the US National Science Foundation. Part of this work was done when J.S. visited the National Central University in May 2009, and he thanks the NCU for their warm hospitality.",

year = "2011",

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doi = "10.1017/S0308210509001115",

language = "English",

volume = "141",

pages = "45--64",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

issn = "0308-2105",

publisher = "Cambridge University Press",

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T1 - Existence, uniqueness and stability of positive solutions to sublinear elliptic systems

AU - Chern, Jann Long

AU - Tang, Yong Li

AU - Lin, Chang Shou

AU - Shi, Junping

N1 - Funding Information: We thank the anonymous referee for helpful suggestions and comments. J.L.C. was partly supported by the National Science Council of Taiwan Grant no. 97-2115-M008-011. J.S. was partly supported by the National Natural Science Foundation of China Grant no. 10671049, the Longjiang Professorship and the US National Science Foundation. Part of this work was done when J.S. visited the National Central University in May 2009, and he thanks the NCU for their warm hospitality.

PY - 2011/2

Y1 - 2011/2

N2 - The existence, stability and uniqueness of positive solutions to a semilinear elliptic system with sublinear nonlinearities are proved. It is shown that the precise global bifurcation diagram of the positive solutions is a monotone curve with different asymptotical behaviour according to the form of the nonlinearities. Equations with Hölder continuous nonlinearities are also considered.

AB - The existence, stability and uniqueness of positive solutions to a semilinear elliptic system with sublinear nonlinearities are proved. It is shown that the precise global bifurcation diagram of the positive solutions is a monotone curve with different asymptotical behaviour according to the form of the nonlinearities. Equations with Hölder continuous nonlinearities are also considered.

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UR - https://www.scopus.com/pages/publications/79960439217#tab=citedBy

U2 - 10.1017/S0308210509001115

DO - 10.1017/S0308210509001115

M3 - Article

AN - SCOPUS:79960439217

SN - 0308-2105

VL - 141

SP - 45

EP - 64

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 1

ER -

Existence, uniqueness and stability of positive solutions to sublinear elliptic systems

Abstract

ASJC Scopus subject areas

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