Asymptotic stability of two classes of second-order integro-differential equations of Volterra type

Iskandarov, S.

doi:10.1134/s0012266108070033

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Cited by 4 publications

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“…To solve this problem, we will develop the method of auxiliary kernels [1,2]. It is worth to note that such problem for other classes of IDEs of the form (1) and with the use of other methods was considered in many works (see, e.g., [3,4]).…”

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confidence: 99%

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On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation

Iskandarov

Abdiraiimova

2020

J Math Sci

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Sufficient conditions for the asymptotic stability of the solutions of a second-order linear integro-differential equation of the Volterra type are established in the case where the solutions of the corresponding second-order linear differential equation may have no property under study. Thus, the influence of integral perturbations on the asymptotic stability of solutions of linear differential equations of the second order is revealed. For this purpose, the method of auxiliary kernels is developed. An illustrative example is given.

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confidence: 99%

“…Then we carry on the integration by parts: With regard for (2) and 3, we get the following loaded IDE from IDE (1):…”

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confidence: 99%