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Periodic solutions and their stability of some higher-order positively homogenous differential equations

Author

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  • Cen, Xiuli
  • Llibre, Jaume
  • Zhang, Meirong

Abstract

In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1,h(t) is a continuous T-periodic function of non-zero average, and μ is a positive small parameter. By using the averaging theory, we will give the existence of T-periodic solutions. Moreover, the instability and the linear stability of these periodic solutions will be obtained.

Suggested Citation

  • Cen, Xiuli & Llibre, Jaume & Zhang, Meirong, 2018. "Periodic solutions and their stability of some higher-order positively homogenous differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 285-288.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:285-288
    DOI: 10.1016/j.chaos.2017.11.032
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