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Qualitative analysis of integro-differential equations with variable retardation

  • * Corresponding author: Martin Bohner

    * Corresponding author: Martin Bohner 
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  • The paper is concerned with a class of nonlinear time-varying retarded integro-differential equations (RIDEs). By the Lyapunov–Krasovski$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{ı} $ functional method, two new results with weaker conditions related to uniform stability (US), uniform asymptotic stability (UAS), integrability, boundedness, and boundedness at infinity of solutions of the RIDEs are given. For illustrative purposes, two examples are provided. The study of the results of this paper shows that the given theorems are not only applicable to time-varying linear RIDEs, but also applicable to time-varying nonlinear RIDEs.

    Mathematics Subject Classification: 34D05, 34K20, 45J05.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  Solution $ x_1 $ of system of RIDEs (9) for different initial values

    Figure 2.  Solution $ x_2 $ of system of RIDEs (9) for different initial values

    Figure 3.  Bounded solution $ x_1 $ of system of RIDEs (11) for different initial values

    Figure 4.  Bounded solution $ x_2 $ of system of RIDEs (11) for different initial values

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