ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH AND WITHOUT RETARDATION

被引：9

作者：

Graef, John R. ^{[1
]}

Tunc, Osman ^{[2
]}

机构：

[1] Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA

[2] Van Yuzuncu Yil Univ, Fac Sci, Dept Math, Van, Turkey

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2021年 / 33卷 / 03期

关键词：

Volterra integro-differential equations; retardation; asymptotic stability; integrability; boundedness; Lyapunov-Krasovskii type functionals;

D O I：

10.1216/jie.2021.33.289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Asymptotic stability, uniform stability, integrability, and boundedness of solutions of Volterra integro- differential equations with and without constant retardation are investigated using a new type of Lyapunov- Krasovskii functionals. An advantage of the new functionals used here is that they eliminate using Gronwall's inequality. Compared to related results in the literature, the conditions here are more general, simple, and convenient to apply. Examples to show the application of the theorems are included.

引用

页码：289 / 300

页数：12

共 50 条

[31] On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order
Tunc, Cemil
Tunc, Osman
MATHEMATICS, 2022, 10 (22)
[32] Study of Volterra Integro-Differential Equations with Kernels Depending on a Parameter
Vlasov, V. V.
Ortiz, R. Perez
Rautian, N. A.
DIFFERENTIAL EQUATIONS, 2018, 54 (03) : 363 - 380
[33] Adaptive collocation methods for Volterra integral and integro-differential equations
Jiang, Yingjun
APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) : 67 - 78
[34] A method for fractional Volterra integro-differential equations by Laguerre polynomials
Dilek Varol Bayram
Ayşegül Daşcıoğlu
Advances in Difference Equations, 2018
[35] EXPONENTIAL STABILITY OF SEMIGROUPS GENERATED BY VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
Rautian, N. A.
UFA MATHEMATICAL JOURNAL, 2021, 13 (04): : 63 - 79
[36] A Novel Numerical Method for Solving Volterra Integro-Differential Equations
Patade J.
Bhalekar S.
International Journal of Applied and Computational Mathematics, 2020, 6 (1)
[37] Study of Volterra Integro-Differential Equations by Methods of Semigroup Theory
Rautian, N. A.
DOKLADY MATHEMATICS, 2023, 108 (02) : 402 - 405
[38] Stability of neutral Volterra integro-differential equations with infinite delay
Li, Xiushuai
Jiang, Jiao
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2023, 4 (02):
[39] A method for fractional Volterra integro-differential equations by Laguerre polynomials
Bayram, Dilek Varol
Dascioglu, Aysegul
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[40] Qualitative behaviour of numerical approximations to Volterra integro-differential equations
Song, YH
Baker, CTH
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 172 (01) : 101 - 115

← 1 2 3 4 5 →