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

Xiuli Cen, Jaume Llibre and Meirong Zhang

Chaos, Solitons & Fractals, 2018, vol. 106, issue C, 285-288

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.

Keywords: Periodic solution; m-Order differential equations; Stability; Averaging theory (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:106:y:2018:i:c:p:285-288

DOI: 10.1016/j.chaos.2017.11.032

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