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

Miled El Hajji

doi:10.1016/j.jksus.2018.11.012

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

Journal article

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

Miled El Hajji

Journal of King Saud University. Science, Vol.31(4), pp.1516-1521

01/10/2019

DOI: https://doi.org/10.1016/j.jksus.2018.11.012

Abstract

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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.

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Title: Boundedness and asymptotic stability of nonlinear Volterra integro-differential equations using Lyapunov functional
Creators - without role: Miled El Hajji - Tunis El Manar University
Publication Details: Journal of King Saud University. Science, Vol.31(4), pp.1516-1521
Publisher: Elsevier
Number of pages: 6
Identifiers: 9933203508331
Academic Unit: University of Jeddah
Language: English
Resource Type: Journal article