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Qualitative investigation of the second order equation x¨+f(x, x¯) x¯+g(x)=0

Published online by Cambridge University Press:  01 September 1997

J. F. JIANG
J. F. JIANG
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, China
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Abstract

This paper investigates the qualitative behaviour of solutions of the second order equation x¨+f(x, x¯) x¯+g(x)=0. The sufficient conditions for all solutions to be oscillatory are established. The theorems on the existence of a nontrivial periodic solution are proved and the criteria for the origin to be a global centre and globally asymptotically stable are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 2 , September 1997 , pp. 325 - 342
Copyright
Cambridge Philosophical Society 1997

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Footnotes

This research was supported by the National Natural Science Foundation of China.