Study of global asymptotic stability in nonlinear neutral dynamic equations on time scales

• Autores: Abdelouaheb Ardjouni, Ahcene Djoudi
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 20, Nº. 3, 2018, págs. 49-63
• Idioma: inglés
• DOI: 10.4067/S0719-06462018000300049
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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].

  • English

    Abstract 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].

• Referencias bibliográficas
  • Adıvar, M.,Raffoul, Y. N.. (2009). Existence of periodic solutions in totally nonlinear delay dynamic equations.. Electronic Journal of Qualitative...
  • Ardjouni, A.,Derrardjia, I.,Djoudi, A.. (2014). Stability in totally nonlinear neutral differential equations with variable delay. Acta Math....
  • Ardjouni, A.,Djoudi, A. (2013). Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale....
  • Ardjouni, A.,Djoudi, A.. (2012). Stability in neutral nonlinear dynamic equations on time scale with unbounded delay. Stud. Univ. Babe¸c-Bolyai...
  • Ardjouni, A.,Djoudi, A.. (2011). Fixed points and stability in linear neutral differential equations with variable delays. Nonlinear Analysis....
  • Belaid, M.,Ardjouni, A.,Djoudi, A.. (2016). Stability in totally nonlinear neutral dynamic equations on time scales. International Journal...
  • Bohner, M.,Peterson, A.. (2001). Dynamic Equations on Time Scales, An Introduction with Applications. Birkhäuser. Boston.
  • Bohner, M.,Peterson, A.. (2003). Advances in Dynamic Equations on Time Scales. Birkhäuser. Boston.
  • Burton, T. A.. (2001). Liapunov functionals, fixed points and stability by Krasnoselskii’s theorem. Nonlinear Stud.. 9. 181
  • Burton, T. A.. (2003). Stability by fixed point theory or Liapunov theory: A Comparaison. Fixed Point Theory. 4. 15-32
  • Burton, T. A.. (2006). Stability by Fixed Point Theory for Functional Differential Equations. Dover Publications. New York.
  • Derrardjia, I.,Ardjouni, A.,Djoudi, A.. (2013). Stability by Krasnoselskii’s theorem in totally nonlinear neutral differential equations....
  • Hilger, S.. (1988). Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. Universität Würzburg. Würzburg.
  • Kaufmann, E. R.,Raffoul, Y. N.. (2007). Stability in neutral nonlinear dynamic equations on a time scale with functional delay. Dynamic Systems...
  • Liu, G.,Yan, J.. (2014). Global asymptotic stability of nonlinear neutral differential equation. Commun Nonlinear Sci Numer Simulat. 19. 1035
  • Smart, D. R.. (1974). Fixed point theorems, Cambridge Tracts in Mathematics. Cambridge University Press. London.
  • Yazgan, R.,Tunc, C.,Atan, O.. (2017). On the global asymptotic stability of solutions to neutral equations of first order. Palestine Journal...