Boundedness and asymptotic stability of nonlinear Volterra integro-differential equations using Lyapunov functional

被引：13

作者：

El Hajji, Miled ^{[1
,2
]}

机构：

[1] Tunis El Manar Univ, ENIT LAMSIN, BP 37, Tunis 1002, Tunisia

[2] Tech & Vocat Training Corp, Gen Studies Dept, Coll Telecom & Elect, Jeddah 2146, Saudi Arabia

来源：

JOURNAL OF KING SAUD UNIVERSITY SCIENCE | 2019年 / 31卷 / 04期

关键词：

BEHAVIOR; MODELS;

D O I：

10.1016/j.jksus.2018.11.012

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, I consider Lyapunov functionals combined with the Laplace transform to obtain boundedness results regarding the solutions of the nonlinear Volterra integro-differential equations x'(t) = A(t)x(t) + B(t) + integral(t)(0) C(t, s)f (x(s))ds + g(x(t)). Asymptotic stability results regarding the zero solution are carried out for the case where B(t)is identically zero. Numerical examples are proposed to perform the given results. (C) 2018 The Author. Production and hosting by Elsevier B.V. on behalf of King Saud University.

引用

页码：1516 / 1521

页数：6

共 50 条

[41] EXPANSION APPROACH FOR SOLVING NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
Rashidinia, J.
Tahmasebi, A.
TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, 2014, 5 (01): : 14 - 27
[42] A series solution of the nonlinear Volterra and Fredholm integro-differential equations
Shidfar, A.
Molabahrami, A.
Babaei, A.
Yazdanian, A.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (02) : 205 - 215
[43] Ulam Stabilities for Nonlinear Volterra Delay Integro-differential Equations
K. D. Kucche
P. U. Shikhare
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2019, 54 : 276 - 287
[44] Numerical Solution of the System of Nonlinear Volterra Integro-differential Equations
Ebadi, G.
Rahimi-Ardabili, M. Y.
Shahmorad, S.
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2009, 33 (05) : 835 - 846
[45] Asymptotic periodicity and almost automorphy for a class of Volterra integro-differential equations
de Andrade, Bruno
Cuevas, Claudio
Henriquez, Erwin
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2012, 35 (07) : 795 - 811
[46] Asymptotic stability of two classes of second-order integro-differential equations of Volterra type
S. Iskandarov
Differential Equations, 2008, 44 : 909 - 922
[47] STABILITY OF NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH CAPUTO FRACTIONAL DERIVATIVE AND BOUNDED DELAYS
Hristova, Snezhana
Tunc, Cemil
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2019,
[48] Asymptotic stability of two classes of second-order integro-differential equations of Volterra type
Iskandarov, S.
DIFFERENTIAL EQUATIONS, 2008, 44 (07) : 909 - 922
[49] Solutions of system of Volterra integro-differential equations using optimal homotopy asymptotic method
Agarwal, Praveen
Akbar, Muhammad
Nawaz, Rashid
Jleli, Mohamed
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (03) : 2671 - 2681
[50] System of Nonlinear Volterra Integro-Differential Equations of Arbitrary Order
Parand, Kourosh
Delkhosh, Mehdi
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2018, 36 (04): : 33 - 54

← 1 2 3 4 5 →