×

A note on positive periodic solutions of delayed differential equations. (English) Zbl 1194.34130

Summary: We consider the existence of positive \(\omega\)-periodic solutions for the periodic equation \(x'(t)=a(t)e^{x(t)}x(t)-\lambda b(t)f(x(t-\tau)))\), where \(a,b\in C(\mathbb R,[0,\infty))\) are \(\omega\)-periodic, \(\int^\infty_0a(t)\,dt>0\), \(\int^\infty_0b(t)\,dt>0\), \(f\in C([0,\infty),[0,\infty))\), and \(f(u)>0\) for \(u>0\), \(\tau(t)\) is a continuous \(\omega\)-periodic function.

MSC:

34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cheng, S.; Zhang, G., Existence of positive periodic solutions for non-autonomous functional differential equations, Electron. J. Differential Equations, 59, 1-8 (2001)
[2] Ye, D.; Fan, M.; Wang, H., Periodic solutions for scalar functional differential equations, Nonlinear Anal., 62, 1157-1181 (2005) · Zbl 1089.34056
[3] Li, Y.; Fan, X.; Zhao, L., Positive periodic solutions of functional differential equations with impulses and a parameter, Comput. Math. Appl., 56, 2556-2560 (2008) · Zbl 1165.34401
[4] Wan, A.; Jiang, D., Existence of positive periodic solutions for functional differential equations, Kyushu J. Math., 56, 193-202 (2002) · Zbl 1012.34068
[5] Wang, H., Positive periodic solutions of functional differential systems, J. Differential Equations, 202, 354-366 (2004) · Zbl 1064.34052
[6] Wu, J.; Wang, Z., Positive periodic solutions of second-order nonlinear differential systems with two parameters, Comput. Math. Appl., 56, 43-54 (2008) · Zbl 1145.34333
[7] Gurney, W. S.; Blythe, S. P.; Nisbet, R. N., Nicholson’s blowflies revisited, Nature, 287, 17-21 (1980)
[8] Wazewska-Czyzewska, M.; Lasota, A., Mathematical problems of the dynamics of a system of red blood cells, Mat. Stosow., 6, 23-40 (1976), (in Polish)
[9] Deimling, K., Nonlinear Functional Analysis (1985), Springer: Springer Berlin · Zbl 0559.47040
[10] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press Orlando, FL · Zbl 0661.47045
[11] Krasnoselskii, M., Positive Solutions of Operator Equations (1964), Noordhoff: Noordhoff Groningen
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.