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

Published online by Cambridge University Press:  11 February 2011

Jann-Long Chern ,
Yong-Li Tang ,
Chang-Shou Lin  and
Junping Shi
Jann-Long Chern
Affiliation:
Department of Mathematics, National Central University, Chung-Li 32001, Taiwan (chern@math.ncu.edu.tw; tangyl@math.ncu.edu.tw)
Yong-Li Tang
Affiliation:
Department of Mathematics, National Central University, Chung-Li 32001, Taiwan (chern@math.ncu.edu.tw; tangyl@math.ncu.edu.tw)
Chang-Shou Lin
Affiliation:
Department of Mathematics, Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan (cslin@math.ntu.edu.tw)
Junping Shi
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA (shij@math.wm.edu)
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Abstract

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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 1 , February 2011 , pp. 45 - 64
Copyright
Copyright © Royal Society of Edinburgh 2011