Existence of positive periodic solutions for delay dynamic equations

  • Faycal Bouchelaghem UBMA.
  • Abdelouaheb Ardjouni University Souk Ahras.
  • Ahcene Djoudi UBMA.

Resumen

In this article we study the existence of positive periodic solutions for a dynamic equations on time scales. The main tool employed here is the Schauder’s fixed point theorem. The results obtained here extend the work of Olach [12]. Two examples are also given to illustrate this work.

Biografía del autor

Faycal Bouchelaghem, UBMA.
Department of Mathematics, Faculty of Sciences.
Abdelouaheb Ardjouni, University Souk Ahras.
Department of Mathematics and Informatics.
Ahcene Djoudi, UBMA.
Applied Mathematics Lab., Faculty of Sciences.

Citas

[1] M. Adivar and Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Differential Equations, No. 1, pp. 1-20, (2009).

[2] A. Ardjouni and A. Djoudi, Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Malaya Journal of Matematik 2 (1), pp. 60-67, (2013).

[3] A. Ardjouni and A. Djoudi, Existence of periodic solutions for nonlin- ear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52, 1, pp. 5-19, (2013).

[4] A. Ardjouni and A. Djoudi, Existence of periodic solutions for non- linear neutral dynamic equations with variable delay on a time scale, Commun Nonlinear Sci Numer Simulat 17, pp. 3061—3069, (2012).

[5] A. Ardjouni and A. Djoudi, Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale, Rend. Sem. Mat. Univ. Politec. Torino Vol. 68, 4, pp. 349-359, (2010).

[6] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An In- troduction with Applications, Birkhäuser, Boston, (2001).

[7] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, (2003).

[8] S. Hilger, Ein Masskettenkalkül mit Anwendung auf Zentrumsman- ningfaltigkeiten. PhD thesis, Universit¨at W¨urzburg, (1988).

[9] E. R. Kaufmann, Y. N. Raffoul, Periodic solutions for a neutral non- linear dynamical equation on a time scale, J. Math. Anal. Appl. 319, pp. 315-325, (2006).

[10] E. R. Kaufmann and Y. N. Raffoul, Periodicity and stability in neutral nonlinear dynamic equation with functional delay on a time scale, Electronic Journal of Differential Equations, No. 27, pp. 1-12, (2007).

[11] V. Lakshmikantham, S. Sivasundaram, B. Kaymarkcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, (1996).

[12] R. Olach, Positive periodic solutions of delay differential equations, Applied Mathematics Letters 26, pp. 1141-1145, (2013).

[13] D. R. Smart, Fixed Points Theorems, Cambridge Univ. Press, Cam- bridge, UK, (1980).
Publicado
2017-10-20
Cómo citar
Bouchelaghem, F., Ardjouni, A., & Djoudi, A. (2017). Existence of positive periodic solutions for delay dynamic equations. Proyecciones. Journal of Mathematics, 36(3), 449-460. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2390
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Artículos