On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation-Reference-Cited by-同舟云学术

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

Published:2020-06-22 Issue:2 Volume:17 Page:188-195
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Iskandarov Samandar¹,Abdiraiimova Nazigai²

Affiliation:

1. Institute of Mathematics of the NAS of the Kyrgyz Republic, Bishkek-71, Kyrgyzstan

2. Osh State University, Osh, Kyrgyzstan

Abstract

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.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

Reference10 articles.

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2. Iskandarov, S. (2008). Asymptotic stability of two classes of integro-differential second-order Volterra equations. Diff. Uravn., 44(7), 883–895 https://doi.org/10.1134/s0012266108070033.

3. Imanaliev, M. I., & Ved’, Yu. A. (1973). Integral perturbations in the theory of stability of systems of differential equations. In: Studies of Integro-Differential Equations in the Kyrgyz Republic, Issue 9, Ilim, Frunze, pp. 3–67 (in Russian).

4. Iskandarov, S. (2002). The Method of Weight and Cutting Functions and Asymptotic Properties of Solutions of Integro-Differential and Integral Volterra-Type Equations. Ilim, Bishkek (in Russian).

5. Iskandarov, S. (2006). On the method of reduction to a system for a linear Volterra integro-differential secondorder equation. In: Studies of Integro-Differential Equations, Issue 35, Ilim, Bishkek, pp. 31–35 (in Russian).