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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
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
Copyright
Copyright © Royal Society of Edinburgh 2011