Existence of periodic solutions for a kind of second-order neutral functional differential equation. (English) Zbl 1059.34043

Lu, Shiping; Ge, Weigao

Appl. Math. Comput. 157, No. 2, 433-448 (2004).

The authors discuss the existence of periodic solutions for a kind of second-order neutral differential equation (NDE), and give several new results on the existence of periodic solutions by means of the continuation theorem of the coincidence degree theory. For discussion of periodic solutions for \(p\)th-order delayed NDEs, we refer to G. He and J. Cao [Appl. Math. Comput. 129, No. 2–3, 391–405 (2002; Zbl 1035.34077) and Appl. Math. Comput. 132, No. 2–3, 231–248 (2002; Zbl 1034.34083)].

Reviewer: Jinde Cao (Nanjing)

MSC:

34K13	Periodic solutions to functional-differential equations
34K40	Neutral functional-differential equations

Keywords:

Periodic solution; Continuation theorem; Neutral functional-differential equation

Citations:

Zbl 1035.34077; Zbl 1034.34083

References:

[1]	Xiankai, H.; Zigui, X., On the existence of 2π-periodic solutions of Duffing type equation \(x^″(t)+g(x(t\)−\(τ)=p(t)\), Chinese Sci. Bull, 39, 3, 201-203 (1994)
[2]	Layton, W., Periodic solutions of a nonlinear delay equations, J. Math. Anal. Appl, 77, 2, 198-204 (1980) · Zbl 0437.34057
[3]	Xiankai, H., On the existence of harmonic solution for the \(n\)-dimensional Liènard equation with delay, J. Sys. Sci. Math. Sci, 19, 3, 328-335 (1999), (in Chinese) · Zbl 0954.34062
[4]	Ma, S. W.; Wang, Z. C.; Yu, J. S., An abstract theorem at resonance and its applications, J. Different. Equat, 145, 2, 274-294 (1998) · Zbl 0940.34056
[5]	Lu, S.; Ge, W., On the existence of periodic solutions of second-order differential equations with deviating arguments, Acta Math. Sin, 45, 4, 811-818 (2002), (in Chinese) · Zbl 1027.34079
[6]	Lu, S.; Ge, W., Periodic solutions for a kind of second-order differential equations with multiple deviating arguments, Appl. Math. Comput, 146, 195-209 (2003) · Zbl 1037.34065
[7]	Wang, G.-Q., A priori bounds for periodic solutions of a delay Rayleigh equation, Appl. Math. Lett, 12, 41-44 (1999) · Zbl 0980.34068
[9]	Hale, J. K.; Mawhin, J., Coincidence degree and periodic solutions of neutral equations, J. Different. Equat, 15, 295-307 (1975) · Zbl 0274.34070
[10]	Fan, M.; Wang, K., Periodic solutions of convex neutral functional differential equations, Tohoku Math. J, 52, 47-49 (2000)
[11]	Hale, J. K., Theory of Functional Differential Equations (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0425.34048
[12]	Bartsch, Th.; Mawhin, J., The Leray-Schauder degree of \(S^1\)-equivariant operator associated to autonomous neutral equations in spaces of periodic functions, J. Different. Equat, 92, 90-99 (1991) · Zbl 0729.34064
[13]	Lu, S., On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments, J. Math. Anal. Appl, 280, 2, 321-333 (2003) · Zbl 1034.34084
[14]	Lu, S.; Ge, W., Existence of positive periodic solutions for neutral functional differential equation with deviating arguments, Appl. Math. J. Chinese Univ. Ser. B, 17, 4, 382-390 (2002) · Zbl 1025.34073
[15]	Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag: Springer-Verlag Berlin · Zbl 0326.34021