Existence of nontrivial periodic solutions for first order functional differential equations. (English) Zbl 1075.34064

Summary: In the case of not requiring the nonlinear terms to be nonnegative, the existence of nontrivial periodic solutions for the first-order functional-differential equations is considered by using the partial ordering theory.


34K13 Periodic solutions to functional-differential equations
Full Text: DOI


[1] Chow, S.N., Remarks on one dimensional delay-differential equations, J. math. anal. appl., 41, 426-429, (1973) · Zbl 0268.34072
[2] Gibbs, H.M.; Hopf, F.A.; Kaplan, D.L.; Shoemaker, R.L., Observation of chaos in optical bistability, Phys. rev. lett., 46, 474-477, (1981)
[3] Hadelar, K.P.; Tomiuk, J., Periodic solutions of differential-difference equations, Arch. ration. mech. anal., 65, 87-95, (1977) · Zbl 0426.34058
[4] Mallet-Paret, J.; Nussbaum, R.D., A differential-delay equation arising in optics and physiology, SIAM J. math., 20, 249-292, (1989) · Zbl 0676.34043
[5] Mallet-Paret, J.; Nussbaum, R.D., Global continuation and asymptotic behavior for periodic solutions of a differential-delay equation, Ann. math. pure. appl, 145, 33-128, (1986) · Zbl 0617.34071
[6] Cheng, S.S.; Zhang, G., Existence of positive periodic solutions for non-autonomous functional differential equations, Electron. J. differential equations, 2001, 59, 1-8, (2001)
[7] Zhang, G.; Cheng, S.S., Positive periodic solutions of nonautonomous functional differential equations depending on a parameter, Abstr. appl. anal., 7, 5, 256-269, (2002)
[8] Jiang, D.Q.; Wei, J.J., Existence of positive periodic solutions of nonautonomous functional differential equations, Chinese ann. math., A20, 6, 715-720, (1999), (in Chinese) · Zbl 0948.34046
[9] Kuang, Y., Delay differential equations with applications in population dynamics, (1993), Academic Press, Inc. · Zbl 0777.34002
[10] Guo, D.J., Nonlinear functional analysis, science and technology press of shandong, (1985), (in Chinese)
[11] Cooke, K.L.; Kaplan, J.L., A periodicity threshold theorem for epidemics and population growth, Math. biosci., 31, 87-104, (1976) · Zbl 0341.92012
[12] Leggett, R.W.; Williams, L.R., A fixed point theorem with application to an infectious disease model, J. math. anal. appl., 76, 91-97, (1980) · Zbl 0448.47044
[13] Agarwal, R.P.; O’Regan, D., Periodic solutions to nonlinear integral equations on the infinite interval modelling infectious disease, Nonlinear anal., 40, 21-35, (2000) · Zbl 0958.45011
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.