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Existence of positive entire solutions for weakly coupled semilinear elliptic systems

Published online by Cambridge University Press:  14 November 2011

Yasuhiro Furusho
Yasuhiro Furusho
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840, Japan
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Synopsis

Weakly coupled semilinear elliptic systems of the form

are considered in RN, N≧2, where k = 1, 2, …, M, u = (u1, …, uM) and λ is a real constant. The aim of this paper is to give sufficient conditions for (*) to have entire solutions whose components are positive in RN and converge to non-negative constants as |x| tends to ∞. For this purpose a new supersolution-subsolution method is developed for the system (*) without any hypotheses on the monotonicity of the non-linear terms fk with respect to u.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 79 - 91
Copyright
Copyright © Royal Society of Edinburgh 1992

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