Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations. (English) Zbl 1101.34054

Summary: We use the coincidence degree theory to establish new results on the existence and uniqueness of \(T\)-periodic solutions for the first-order neutral functional-differential equation \[ (x(t)+Bx(t-\delta))'=g_1(t,x(t))+g_2(t,x(t-\tau))+p(t). \]


34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
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[1] Burton, T. A., Stability and Periodic Solution of Ordinary and Functional Differential Equations (1985), Academic Press: Academic Press Orland, FL · Zbl 0635.34001
[2] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1964), Cambridge Univ. Press: Cambridge Univ. Press London · Zbl 0634.26008
[3] Gaines, R. E.; Mawhin, J., Coincide Degree and Nonlinear Differential Equations, Lecture Notes in Math., vol. 568 (1977), Springer · Zbl 0326.34021
[4] Hale, J. K., Theory of Functional Differential Equations (1977), Springer: Springer New York · Zbl 0425.34048
[5] Hale, J. K.; Mawhin, J., Coincide degree and periodic solutions of neutral equations, J. Differential Equations, 15, 295-307 (1975) · Zbl 0274.34070
[6] Komanovskii, V. B.; Nosov, V. R., Stability of Functional Differential Equations (1986), Academic Press: Academic Press London · Zbl 0593.34070
[7] Kuang, Y., Delay Differential Equations with Applications in Population Dynamical system (1993), Academic Press: Academic Press New York
[8] Lu, S.; Ge, W., On existence of periodic solutions for neutral differential equation, Nonlinear Anal., 54, 1285-1306 (2003) · Zbl 1037.34064
[9] Lu, S.; Ge, W., Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument, Nonlinear Anal., 56, 501-514 (2004) · Zbl 1078.34048
[10] Zhang, M., Periodic solutions of linear and quasilinear neutral functional differential equations, J. Math. Anal. Appl., 189, 378-392 (1995) · Zbl 0821.34070
[11] Wang, G., Existence of periodic solutions for second order nonlinear neutral delay equations, Acta Math. Sinica, 47, 379-384 (2004), (in Chinese) · Zbl 1387.34100
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