Periodicity and stability in neutral nonlinear differential equations by Krasnoselskii’s fixed point theorem

• Autores: Bouzid Mansouri, Abdelouaheb Ardjouni, Ahcene Djoudi
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 19, Nº. 3, 2017, págs. 15-29
• Idioma: inglés
• DOI: 10.4067/S0719-06462017000300015
• Enlaces
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• Resumen
  • español

    Resumen La ecuación diferencial funcional no-lineal neutral con retardo variable =p(t)-a(t)u(t)-a(t)q(t)g(u(t-r(t)))-b(t)f(u(t))+b(t)q(t)f(u(t-r(t))). es investigada. Usando el teorema del punto fijo de Krasnoselskii obtenemos la existencia y la estabilidad asintótica de las soluciones periódicas. Se establecen condiciones suficientes para la existencia y la estabilidad de soluciones de la ecuación anterior. Nuestros resultados extienden algunos de los resultados obtenidos en (19).

  • English

    Abstract The nonlinear neutral functional differential equation with variable delay =p(t)-a(t)u(t)-a(t)q(t)g(u(t-r(t)))-b(t)f(u(t))+b(t)q(t)f(u(t-r(t))). is investigated. By using Krasnoselskii’s fixed point theorem we obtain the existence and the asymptotic stability of periodic solutions. Sufficient conditions are established for the existence and the stability of the above equation. Our results extend some results obtained in the work (19).

• Referencias bibliográficas
  • Ardjouni, A.. (2014). Existence of periodic solutions for a second-order nonlinear neutral differential equation with variable delay. Palestine...
  • Ardjouni, A.. (2014). Existence of positive periodic solutions for two types of third-order nonlinear neutral differential equations with...
  • Ardjouni, A.. (2012). Existence of positive periodic solutions for a nonlinear neutral differential equations with variable delay. Applied...
  • Ardjouni, A.. (2012). Existence of periodic solutions for a second order nonlinear neutral differential equation with functional delay. Electronic...
  • Ardjouni, A.. (2011). Periodic solutions for a second-order nonlinear neutral differential equation with variable delay. Electron. J. Differential...
  • Ardjouni, A.. (2010). Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale. Rend. Sem. Mat. Univ....
  • Burton, T. A.. (2002). Liapunov functionals, fixed points and stability by Krasnoselskii’s theorem. Nonlinear Stud.. 9. 181
  • Burton, T. A.. (2006). Stability by Fixed Point Theory for Functional Differential Equations. Dover Publications. New York.
  • Candan, T.. (2017). Existence of positive periodic solutions of first-order neutral differential equations. Math. Methods Appl. Sci.. 40....
  • Candan, T.. (2016). Existence of positive periodic solutions of first-order neutral differential equations with variable coefficients. Applied...
  • Chen, F. D.. (2005). Positive periodic solutions of neutral Lotka-Volterra system with feedback control. Appl. Math. Comput.. 162. 1279
  • Chen, F. D.. (2005). Periodicity in a nonlinear predator-prey system with state dependent delays. Acta Math. Appl. Sin. Engl. Ser.. 21. 49-60
  • Cheng, Z.. (2014). Existence of positive periodic solution for variable-coefficient third-order differential equation with singularity. Math....
  • Cheng, Z.. Multiplicity Results for variable-coefficient singular third-order differential equation with a parameter. Abstract and Applied...
  • Cheng, S.. (2001). Existence of positive periodic solutions for non-autonomous functional differential equations. Electron. J. Differential...
  • Deham, H.. (2008). Periodic solutions for nonlinear differential equation with functional delay. Georgian Mathematical Journal. 15. 635
  • Deham, H.. (2010). Existence of periodic solutions for neutral nonlinear differential equations with variable delay. Electronic Journal of...
  • Dib, Y. M.. (2005). Periodicity and stability in neutral nonlinear differential equations with functional delay. Electronic Journal of Differential...
  • Ding, L.. (2010). Periodicity and stability in neutral equations by krasnoselskii’s fixed point theorem. Nonlinear Analysis: Real World Applications....
  • Fan, M.. (2003). Periodicity and stability in periodic n-species Lotka-Volterra competition system with feedback controls and deviating arguments....
  • Freedman, H. I.. (1992). Periodic solutions of single-species models with periodic delay. SIAM J. Math. Anal.. 23. 689-701
  • Kuang, Y.. (1993). Delay Differential Equations with Application in Population Dynamics. Academic Press. New York.
  • Li, W. G.. (1997). An constructive proof of the existence Theorem for periodic solutions of Duffng equations. Chinese Sci. Bull.. 42. 1591
  • Liu, Y.. (2004). Positive periodic solutions of nonlinear Duffing equations with delay and variable coefficients. Tamsui Oxf. J. Math. Sci.....
  • Nouioua, F.. (2016). Periodic solutions for a third-order delay differential equation. Applied Mathematics E-Notes. 16. 210
  • Ren, J.. (2011). Positive periodic solutions for third-order nonlinear differential equations. Electron. J. Differential Equations. 2011....
  • Smart, D. R.. (1980). Fixed Points Theorems. Cambridge University Press. Cambridge.
  • Wang, Q.. (1996). Positive periodic solutions of neutral delay equations. Acta Math. Sinica (N.S.). 6. 789
  • Wang, Y.. (2007). Periodic solutions for a second order nonlinear functional differential equation. Applied Mathematics Letters. 20. 110
  • Zeng, W.. (1997). Almost periodic solutions for nonlinear Duffing equations. Acta Math. Sinica (N.S.). 13. 373
  • Zhang, G.. (2002). Positive periodic solutions of non autonomous functional differential equations depending on a parameter. Abstr. Appl....