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The stability of RDDE\(\ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O\)

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Abstract

In this paper, the author considered the stability of zero solution of linear RDDE

$$\begin{gathered} \ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O, \hfill \\ \ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) = O \hfill \\ \end{gathered} $$

using Liapunov-Razumikhin functional and transformations and obtained some sufficient conditions for the stability of Eqs.(1) and (2). These results are suitable both for boundedp i (t),q i (t) andr(t).i=1,2.

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Authors and Affiliations

  1. Anhui University, Hefei

    Huang Wengang

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  1. Huang Wengang
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Huang, W. The stability of RDDE\(\ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O\) . Acta Mathematicae Applicatae Sinica 7, 279–283 (1991). https://doi.org/10.1007/BF02005976

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  • DOI: https://doi.org/10.1007/BF02005976

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