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Necessary and sufficient conditions for the existence of equilibrium in abstract non-autonomous functional differential equations

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Abstract

In this article, we aim to establish necessary and sufficient conditions that guarantee the existence of equilibria and continuous equilibria for the continuous skew-product semiflow induced by a class of abstract non-autonomous finite-delay functional differential equations without any monotone conditions assumed. A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained. Several illustrative examples are employed to demonstrate our results.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    ZuoHuan Zheng

  2. College of Mathematics and Information Sciences, Shandong Institute of Business and Technology, Yantai, 264005, China

    XiLiang Li

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  1. ZuoHuan Zheng
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  2. XiLiang Li
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Correspondence to XiLiang Li.

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Zheng, Z., Li, X. Necessary and sufficient conditions for the existence of equilibrium in abstract non-autonomous functional differential equations. Sci. China Math. 53, 2045–2059 (2010). https://doi.org/10.1007/s11425-010-3012-0

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