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Boundedness results for impulsive functional differential equations with infinite delays

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Abstract

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form

$$\begin{gathered} x'(t) = F(t,x( \cdot )), t > t^ * \hfill \\ \Delta x(t_k ) = I(t_k ,x(t_k^ - )), k = 1,2,... \hfill \\ \end{gathered} $$

By using Lyapunov functions and Razumikhin technique, some new Bazumikhin-type theorems on boundedness are obtained.

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Authors and Affiliations

  1. School of Science, Jinan University, 250022, Shandong Province, China

    Hua Li

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  1. Hua Li
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  2. Zhiguo Luo
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Correspondence to Hua Li.

Additional information

Hua Li received her master's degree at Hunan Normal University under the direction of Zhiguo Luo in June 2004. She has been at Jinan University after graduation. Her research interests focus on qualitative theory of functional differential equations.

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Li, H., Luo, Z. Boundedness results for impulsive functional differential equations with infinite delays. JAMC 18, 261–272 (2005). https://doi.org/10.1007/BF02936570

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  • DOI: https://doi.org/10.1007/BF02936570

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