On strongly decreasing solutions of cyclic systems of second-order nonlinear differential equations

The n-dimensional cyclic system of second-order nonlinear differential equations is analysed in the framework of regular variation. Under the assumption that αi and βi are positive constants such that α1 … αn > β1 … βn and pi and qi are regularly varying functions, it is shown that the situation...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2015-10, Vol.145 (5), p.1007-1028
Main Authors: Jaros, Jaroslav, TakaÅi, Kusano
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Constants
Decomposition
Differential equations
Nonlinear equations
Nonlinearity
Partial differential equations
Symmetry
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Summary:The n-dimensional cyclic system of second-order nonlinear differential equations is analysed in the framework of regular variation. Under the assumption that αi and βi are positive constants such that α1 … αn > β1 … βn and pi and qi are regularly varying functions, it is shown that the situation in which the system possesses decreasing regularly varying solutions of negative indices can be completely characterized, and moreover that the asymptotic behaviour of such solutions is governed by a unique formula describing their order of decay precisely. Examples are presented to demonstrate that the main results for the system can be applied effectively to some classes of partial differential equations with radial symmetry to provide new accurate information about the existence and the asymptotic behaviour of their radial positive strongly decreasing solutions.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210515000244