Existence of positive periodic solutions for delay dynamic equations.
Keywords:
Positive periodic solutions, Schauder’s fixed point theorem, Dynamic equations, Time scalesAbstract
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.
References
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 nonlinear 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 Introduction 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, Universität Würzburg, (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, Cambridge, UK, (1980).
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.