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Periodic Solutions for a Class of Forced Liénard-type Equations

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Abstract

By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Liénard-type equation

$$ {x}\ifmmode{''}\else$''$\fi + {\sum\limits_{i = 1}^n {h_{i} {\left( x \right)}{\left| {{x}\ifmmode{'}\else$'$\fi} \right|}^{{2\alpha _{i} }} + f_{1} {\left( x \right)}{\left| {{x}\ifmmode{'}\else$'$\fi} \right|}^{2} + f_{2} {\left( x \right)}{x}\ifmmode{'}\else$'$\fi + g{\left( {t,x} \right)} = p{\left( t \right)}.} } $$

Our results extend and improve some known results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Hunan University of Arts and Science, Changde, Hunan 415000, China

    Bing-wen Liu

  2. College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

    Li-hong Huang

Authors
  1. Bing-wen Liu
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  2. Li-hong Huang
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Correspondence to Bing-wen Liu.

Additional information

Supported by the National Natural Science Foundation of China (No. 10371034), the Doctor Program Foundation of the Ministry of Education of China (20010532002) and Key Object of Chinese Ministry of Education ([2002]78).

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Liu, Bw., Huang, Lh. Periodic Solutions for a Class of Forced Liénard-type Equations. Acta Mathematicae Applicatae Sinica, English Series 21, 81–92 (2005). https://doi.org/10.1007/s10255-005-0218-y

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  • DOI: https://doi.org/10.1007/s10255-005-0218-y

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