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A criterion of the non-existence of periodic solutions for a generalized li énard system and its applications

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Abstract

In this paper, a new criterion of the non-existence of periodic solutions for a generalized liénard system

$$\left\{ {\begin{array}{*{20}c} {\dot x = P(Q(y) - F(x))} \\ {\dot y = - g(x)} \\ \end{array} } \right.$$

is given, which generalizes and extends some known results of Sugie et al. The results can be applied to the well-known nonlinear oscillating equation ẍ+f(x)h(ẋ)ẋ+g(x)k(ẋ)=0, and the criterion of the non-existence of periodic solutions associated with this equation is obtained.

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Authors and Affiliations

  1. Dept. of Appl. Math. and Phys., Hebei Univ. of Technology, 30013, Tianjin

    Zhou Jin & Xiang Lan

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  1. Zhou Jin
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  2. Xiang Lan
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Jin, Z., Lan, X. A criterion of the non-existence of periodic solutions for a generalized li énard system and its applications. Appl. Math. Chin. Univ. 14, 15–20 (1999). https://doi.org/10.1007/s11766-999-0050-x

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  • DOI: https://doi.org/10.1007/s11766-999-0050-x

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