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Cubo (Temuco)
versión On-line ISSN 0719-0646
Cubo vol.20 no.3 Temuco oct. 2018
http://dx.doi.org/10.4067/S0719-06462018000300049
Articles
Study of global asymptotic stability in nonlinear neutral dynamic equations on time scales
1University of Souk Ahras, Department of Mathematics and Informatics, P.O. Box 1553, Souk Ahras, 41000, Algeria. abd_ardjouni@yahoo.fr
2University of Annaba, Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, P.O. Box 12, Annaba 23000, Algeria. adjoudi@yahoo.com
This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral dynamic equations in C1 rd. By converting the nonlinear neutral dynamic equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle. The results obtained here extend the work of Yazgan, Tunc and Atan [17].
Keywords and Phrases: Fixed points; neutral dynamic equations; asymptotic stability; time scales
Este artículo está mayormente interesado en la estabilidad global asintótica de la solución cero de una clase de ecuaciones nolineales neutrales dinámicas en C1 rd. Transformando la ecuación nolineal neutral dinámica en una ecuación integral equivalente, nuestros resultados principales son obtenidos a través del principio de la aplicación contractiva de Banach. Los resultados obtenidos aquí son una extensión del trabajo de Yazgan, Tunc y Atan [17].
Acknowledgments.
The authors would like to thank the anonymous referee for his/her valuable remarks.
References
[1] M. Adıvar, Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations. Electronic Journal of Qualitative Theory of Differential Equations 2009, 1 (2009), 1-20. [ Links ]
[2] A. Ardjouni, I. Derrardjia and A. Djoudi, Stability in totally nonlinear neutral differential equations with variable delay, Acta Math. Univ. Comenianae, Vol. LXXXIII, 1 (2014), pp. 119-134. [ Links ]
[3] A. Ardjouni , A Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52, 1 (2013) 5-19. [ Links ]
[4] A. Ardjouni , A. Djoudi , Stability in neutral nonlinear dynamic equations on time scale with unbounded delay, Stud. Univ. Babe¸c-Bolyai Math. 57(2012), No. 4, 481-496. [ Links ]
[5] A. Ardjouni , A. Djoudi , Fixed points and stability in linear neutral differential equations with variable delays, Nonlinear Analysis 74 (2011), 2062-2070. [ Links ]
[6] M. Belaid, A. Ardjouni andA. Djoudi , Stability in totally nonlinear neutral dynamic equations on time scales, International Journal of Analysis and Applications, Vol. 11, Nu. 2 (2016), 110-123. [ Links ]
[7] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001. [ Links ]
[8] M. Bohner , A. Peterson , Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston , 2003. [ Links ]
[9] T. A. Burton, Liapunov functionals, fixed points and stability by Krasnoselskii’s theorem, Nonlinear Stud. 9 (2001), 181-190. [ Links ]
[10] T. A. Burton, Stability by fixed point theory or Liapunov theory: A Comparaison, Fixed Point Theory, 4(2003), 15-32. [ Links ]
[11] T. A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006. [ Links ]
[12] I. Derrardjia, A. Ardjouni andA. Djoudi , Stability by Krasnoselskii’s theorem in totally nonlinear neutral differential equations, Opuscula Math. 33(2) (2013), 255-272. [ Links ]
[13] S. Hilger, Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph. D. thesis, Universität Würzburg, Würzburg, 1988. [ Links ]
[14] E. R. Kaufmann, Y. N. Raffoul , Stability in neutral nonlinear dynamic equations on a time scale with functional delay, Dynamic Systems and Applications 16 (2007) 561-570. [ Links ]
[15] G. Liu, J. Yan, Global asymptotic stability of nonlinear neutral differential equation, Commun Nonlinear Sci Numer Simulat 19 (2014) 1035-1041. [ Links ]
[16] D. R. Smart, Fixed point theorems, Cambridge Tracts in Mathematics, no. 66, Cambridge University Press, London-New York, 1974. [ Links ]
[17] R. Yazgan, C. Tunc and O. Atan, On the global asymptotic stability of solutions to neutral equations of first order, Palestine Journal of Mathematics, Vol. 6(2) (2017), 542-550. [ Links ]
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