On Stability and Asymptotic Stability of Solutions for a Linear Fourth Order Volterra Integro-Differential Equation on the Half-Axis

被引：0

作者：

Iskandarov, S. ^{[1
]}

Khalilov, A. T. ^{[1
]}

机构：

[1] Natl Acad Sci Kyrgyz Republ, Inst Math, Bishkek 720071, Kyrgyzstan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 07期

关键词：

Volterra integro-differential equation of the fourth order; stability of solutions; asymptotic stability of solutions; non-standard reduction to a system; Lyapunov functional; squaring the equation; BOUNDARY-VALUE PROBLEM;

D O I：

10.1134/S199508022307020X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sufficient conditions for the stability and asymptotic stability of solutions of a linear integro-differential equation of the fourth order of the Volterra type on the semiaxis are established. For this, the following are developed: a non-standard method of reduction to a system, the method of Lyapunov functionals, the method of integro-differential inequalities, the method of integral inequalities, as well as the method of squaring equations, and the Lyusternik-Sobolev lemma is applied. An illustrative example is being built.

引用

页码：2707 / 2714

页数：8

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