Structure of the set of bounded  solutions  for a class of  nonautonomous  second order                differential equations

Yuan Guo; Xiaofei Gao; Desheng Li

doi:10.3934/cpaa.2010.9.1607

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2010, Volume 9, Issue 6: 1607-1616. Doi: 10.3934/cpaa.2010.9.1607

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Structure of the set of bounded solutions for a class of nonautonomous second order differential equations

1.
Department of Mathematics, Lanzhou City University, Lanzhou 730070
2.
Department of Mathematics, Tianjin University, Tianjin 300072

Received: April 30, 2009

Revised: April 30, 2010

Published: October 2010

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Abstract

Some precise descriptions of the structure and behavior of bounded solutions for a class of nonautonomous second order differential equations $x''+g(x)x'+f(\theta_t h,x)=0$ are investigated. The results contain many previous ones in the literature as particular cases.

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Mathematics Subject Classification: Primary: 34C11, 34D05; Secondary: 37C60.

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