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Applied Mathematics and Mechanics

, Volume 17, Issue 4, pp 385–392 | Cite as

Research of the periodic solution for a class of nonlinear differential equations

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Abstract

In this paper, we study the existence, uniqueness and asymptotic stability of the periodic solution for a class of the most-universal fourth-order nonlinear nonautonomous periodic systems. We give the relevant Liapunov function by using the method of analogical slowly changing coefficients. We also give a considerably accurate estimation of the slowly changing coefficients and obtain the sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions.

Key words

fourth-order nonlinear system periodic solution existence and uniqueness asymptotic stability 

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References

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    Wong Rongliang, Existence and stability of periodic solutions for a class of nonlinear and nonautonomy system of three orders, Kexue Tongbao, 32, 16 (1987).Google Scholar
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    Jin Jun. The existence and uniqueness of periodic solutions for nonlinear periodic systems with slowly changing coefficients, Journal of Mathematical Research and Exposition, 11, 2 (1991). (in Chinese)Google Scholar
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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Jin Jun
    • 1
  1. 1.Shanghai Teachers UniversityShanghaiP. R. China

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