Positive periodic solutions for neutral functional differential systems

Ernest Yankson, Samuel E. Assabil


We study the existence of positive periodic solutions of a system of neutral differential equations. In the process we construct two map- pings in which one is a contraction and the other compact. A Kras- noselskii’s fixed point theorem is then used in the analysis.

Palabras clave

Stability theory; Integro-ordinary differential equations; Volterra integral equations.

Texto completo:



T. A. Burton, Stability by Fixed Point Theory for functional Differ- ential Equations, Dover, New York, (2006).

E. Beretta, F. Solimano, Y. Takeuchi, A mathematical model for drug administration by using the phagocytosis of red blood cells, J. Math Biol. 10 Nov;35 (1), pp. 1-19, (1996).

Y. Chen, New results on positive periodic solutions of a periodic integro-differential competition system, Appl. Math. Comput., 153 (2), pp. 557-565, (2004).

F. D. Chen, Positive periodic solutions of neutral Lotka-Volterra sys- tem with feedback control, Appl. Math. Comput., 162 (3), pp. 1279- 1302, (2005).

F. D. Chen, Periodicity in a nonlinear predator-prey system with state dependent delays, Acta Math. Appl. Sinica English Series, 21 (1) (2005), pp. 49-60, (2005).

F. D. Chen, S. J. Lin, Periodicity in a logistic type system with several delays, Comput. Math. Appl., 48 (1-), pp. 35-44, (2004).

F. D. Chen, F. X. Lin, X. X. Chen, Sufficient conditions for the ex- istence of positive periodic solutions of a class of neutral delay mod- els with feedback control, Appl. Math. Comput., 158 (1), pp. 45-68, (2004).

M. Fan, K. Wang, Global periodic solutions of a generalized n-species Gilpin-Ayala competition model, Comput. Math. Appl., 40, pp. 1141- 1151, (2000).

M. Fan, P. J. Y. Wong, Periodicity and stability in a periodic n-species Lotka-Volterra competition system with feedback controls and deviat- ing arguments, Acta Math. Sinica,, 19 (4), pp. 801-822, (2003).

M. E. Gilpin, F. J. Ayala, Global Models of Growth and Competition, Proc. Natl. Acad. Sci., USA 70, pp. 3590-3593, (1973).

A. Datta and J. Henderson, Differences and smoothness of solutions for functional difference equations, Proceedings Difference Equations 1, pp. 133-142, (1995).

J. Henderson and A. Peterson, Properties of delay variation in solu- tions of delay difference equations, Journal of Differential Equations 1, pp. 29-38, (1995).

D. Jiang, J. wei, B. Zhang, Positive periodic solutions of functional differential equations and population models, Electron. J. Diff.Eqns., Vol. No. 71, pp. 1-13, (2002).

M. A. Krasnosel’skii, Positive solutions of operator Equations Noord- hoff, Groningen, (1964).

L. Y. Kun, Periodic solution of a periodic neutral delay equation, J. Math. Anal. Appl.,, 319, pp. 315-325, (2006).

Y. Li, Y. Kuang, Periodic solutions of periodic delay Lotka-Volterra equations and systems, J. Math. Anal. Appl.,, 255, pp. 260-280, (2001).

M. Maroun and Y. Raffoul , Periodic solutions in nonlinear neutral difference equations with functional delay, Journal of Korean Mathe- matical Society 42, pp. 255-268, (2005).

Y. Raffoul, Periodic solutions for scaler and vector nonlinear differ- ence equations, Pan-American Journal of Mathematics 9, pp. 97-111, (1999).

Y. N. Raffoul, Periodic solutions for neutral nonlinear differential equa- tions with delay, Electron. J. Diff. Eqns., Vol. No. 102, pp. 1-7, (2003).

Y. Raffoul, Positive periodic solutions in neutral nonlinear differen- tial equations, Electronic Journal of Qualitative Theory of Differential Equations 16, pp. 1-10, (2007).

Y. Raffoul, Existence of positive periodic solutions in neutral nonlinear equations with functional delay, Rocky Mount. Journal ofMathematics 42(6), pp. 1983-1993, (2012).

N. Zhang, B. Dai, Y. Chen, Positive periodic solutions of nonau- tonomous functional differential systems, J. Math. Anal., 333, pp. 667- 678, (2007).

Enlaces refback

  • No hay ningún enlace refback.