Existence of positive periodic solutions for delay dynamic equations

Faycal Bouchelaghem, Abdelouaheb Ardjouni, Ahcene Djoudi

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.

Palabras clave


Positive periodic solutions; Schauder’s fixed point theo- rem; Dynamic equations; Time scales.

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Referencias


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).

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).

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).

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).

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).

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

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

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

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).

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).

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

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

D. R. Smart, Fixed Points Theorems, Cambridge Univ. Press, Cam- bridge, UK, (1980).


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