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Periodic Solutions for a Class of Second-Order Ordinary Differential Equations

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Abstract

This paper is devoted to the study of periodic solutions for a class of second-order ordinary differential equations by utilizing a technique for obtaining solutions to free problems in the calculus of variations originating in the work of Carathéodory (Ref. 1, 1935). The key of this technique is to find some suitable transformation which transfers the periodic solution problem to an equivalent variational problem in which the minimizer is more easily determined. Some applications are presented to illustrate the utility of this technique.

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, Changchun, China

    S. G. Ji PhD

  2. College of Mathematics, Jilin University, Changchun, China

    S. Y. Shi (Professor)

Authors
  1. S. G. Ji PhD
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  2. S. Y. Shi
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Additional information

Communicated by D. A. Carlson

Supported by NSFC Grant 10401013, 985 Project of Jilin University and Graduate Innovation Lab of Jilin University. The authors thank Professor D. A. Carlson and the anonymous referees for valuable suggestions and helpful comments.

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Ji, S.G., Shi, S.Y. Periodic Solutions for a Class of Second-Order Ordinary Differential Equations. J Optim Theory Appl 130, 125–137 (2006). https://doi.org/10.1007/s10957-006-9092-x

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  • DOI: https://doi.org/10.1007/s10957-006-9092-x

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