On the attractivity of an integrodifferential system with state-dependent delay

Volume 12, Issue 9, pp 611--620 http://dx.doi.org/10.22436/jnsa.012.09.06

Publication Date: May 24, 2019 Submission Date: November 18, 2018 Revision Date: February 22, 2019 Accteptance Date: April 04, 2019

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Authors

Kora Hafiz Bete - Universite d'Abomey-Calavi, Institut de Mathematiques et de Sciences Physiques, 01 B.P. 613, Porto-Novo, Benin. Carlos Ogouyandjou - Universite d'Abomey-Calavi, Institut de Mathematiques et de Sciences Physiques, 01 B.P. 613, Porto-Novo, Benin. Amadou Diop - Universite Gaston Berger de Saint-Louis, UFR SAT, Departement de Mathematiques, B.P. 234, Saint-Louis, Senegal. Mamadou Abdoul Diop - Universite Gaston Berger de Saint-Louis, UFR SAT, Departement de Mathematiques, B.P. 234, Saint-Louis, Senegal.

Abstract

This work is focused on the existence and attractivity of mild solutions for an integrodifferential system with state-dependent delay. The results presented here were established by means of a fixed point theorem due to [T. A. Burton, C. Kirk, Math. Nachr., \(\bf189\) (1998), 23--31]. At the end, the obtained results are illustrated by an example.

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ISRP Style

Kora Hafiz Bete, Carlos Ogouyandjou, Amadou Diop, Mamadou Abdoul Diop, On the attractivity of an integrodifferential system with state-dependent delay, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 9, 611--620

AMA Style

Bete Kora Hafiz, Ogouyandjou Carlos, Diop Amadou, Diop Mamadou Abdoul, On the attractivity of an integrodifferential system with state-dependent delay. J. Nonlinear Sci. Appl. (2019); 12(9):611--620

Chicago/Turabian Style

Bete, Kora Hafiz, Ogouyandjou, Carlos, Diop, Amadou, Diop, Mamadou Abdoul. "On the attractivity of an integrodifferential system with state-dependent delay." Journal of Nonlinear Sciences and Applications, 12, no. 9 (2019): 611--620

Keywords

Neutral functional integrodifferential equations
resolvent operator
mild solution
local attractivity
fixed point theory
infinite delay

MSC

34G20
34K10
34K30

References

[1] K. Balachandran, R. R. Kumar, Existence of solutions of integrodifferential evolution equations with time varying delays, Appl. Math. E-Notes, 7 (2007), 1--8

[2] J. Banaś, B. C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal., 69 (2008), 1945--1952

[3] On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Banaś, B. Rzepka, J. Math. Anal. Appl., 284 (2003), 165--173

[4] J. Banaś, T. Zaja̧c, Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear Anal., 71 (2009), 5491--5500

[5] T. A. Burton, C. Kirk, A fixed point theorem of Krasnoselski--Schaefer type, Math. Nachr., 189 (1998), 23--31
- View Article
- Google Scholar

[6] C. Corduneanu, Integral equations and stability of feedback systems, Academic Press, New York-London (1973)

[7] K. Ezzinbi, S. Ghnimi, Existence and regularity of solutions for neutral partial functional integrodifferential equations, Nonlinear Anal. Real World Appl., 11 (2010), 2335--2344

[8] K. Ezzinbi, S. Ghnimi, M. A. Taoudi, Existence and regularity of solutions for neutral partial functional integrodifferential equations with infinite delay, Nonlinear Anal. Hybrid Syst., 4 (2010), 54--64

[9] K. Ezzinbi, H. Toure, I. Zabsonre, Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach space, Nonlinear Anal., 70 (2009), 3378--3389

[10] Y. Fujita, Integrodifferential equation which interpolates the heat equation and tne wave equation, Osaka J. Math., 27 (1990), 309--321
- View Article
- Google Scholar

[11] R. C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc., 273 (1982), 333--349

[12] J. K. Hale, J. J. Kato, Phase spaces for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11--41

[13] J. K. Hale, S. M. Verduyn Lunel, Introduction to functional differential equations, Springer-Verlag, New York (1993)

[14] F. Hartung, J. Turi, Identification of parameters in delay equations with state--dependent delays, Nonlinear Anal., 29 (1997), 1303--1318

[15] E. Hernández M., M. A. McKibben, On state--dependent delay partial neutral functional--differential equations, Appl. Math. Comput., 186 (2007), 294--301

[16] Y. Hino, S. Murakami, T. Naito, Functional differential equations with unbounded delay, Springer-Verlag, Berlin (1991)
- View Article

[17] J. Liang, J. H. Liu, T.-J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Modelling, 49 (2009), 798--804

[18] A. M. Lyapunov, The general problem of the stability of Motion (Translated by A. T. Fuller from Edouard Davaux's French translation (1907) of the 1892 Russian original), Internat. J. Control, 55 (1992), 531--534

[19] N. I. Mahmudov, Existence and uniqueness results for neutral SDEs in Hilbert spaces, Stoch. Anal. Appl., 24 (2006), 79--95