×

Positive periodic solutions for a periodic neutral differential equation with feedback control. (English) Zbl 1092.34033

Sufficient conditions are derived for the existence of periodic solutions of a periodic single species model governed by a neutral differential equation with feedback control. The approach is based on the abstract continuation theory for \(k\)-contractions.

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
92D25 Population dynamics (general)
47H11 Degree theory for nonlinear operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gaines, R. E.; Mawhin, J. L., (Lecture Notes in Mathematics, vol. 586 (1977), Springer: Springer Berlin)
[2] Gopalsamy, K., Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0752.34039
[3] Hetzer, G., Some remarks on \(\Phi_+\) operators and the coincidence degree for Fredholm equations with noncompact nonlinear perturbations, Ann. Soc. Sci. Bruxelles, 89, IV, 508-847 (1975) · Zbl 0316.47041
[4] Li, Y. K.; Liu, P.; Zhu, L. F., Positive periodic solutions of a class of functional differential systems with feedback controls, Nonlinear Anal., 57, 655-666 (2004) · Zbl 1064.34049
[5] Petryshyn, W. V.; Yu, Z. S., Existence theorems for higher order nonlinear periodic boundary value problems, Nonlinear Anal., 6, 9, 943-969 (1982) · Zbl 0525.34015
[6] Weng, P., Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls, Comput. Math. Appl., 40, 747-759 (2000) · Zbl 0962.45003
[7] Yang, F.; Jiang, D. Q., Existence and global attractivity of positive periodic solution of a logistic growth system with feedback control and deviating arguments, Ann. Differential Equations, 17, 4, 377-384 (2001) · Zbl 1004.34030
[8] Yin, F. Q.; Li, Y. K., Positive periodic solutions of a single species model with feedback regulation and disturbed time delay, Appl. Math. Comput., 153, 475-484 (2004) · Zbl 1087.34051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.