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Stability of linear differential equations with a distributed delay

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  • We present some new stability results for the scalar linear equation with a distributed delay

    $\dot{x}(t) + \sum_{k=1}^m \int_{h_k(t)}^t x(s) d_s R_k(t,s) =0, h_k(t)\leq t,$ su$p_{t\geq 0}(t-h_k(t))<\infty,$

    where the functions involved in the equation are not required to be continuous.
    The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.

    Mathematics Subject Classification: Primary: 34K20; Secondary: 34K25.


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