Resonant and nonresonant oscillations of certain third-order differential equations with delay. (English) Zbl 0792.34069
Wiener, Joseph (ed.) et al., Ordinary and delay differential equations 1. Proceedings of the international conference on theory and applications of differential equations, held at the University of Texas-Pan American, Edinburg, TX, USA, on May 15-18, 1991. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 272, 238-243 (1993).
In continuation of his study in [J. Nigerian Math. Soc. 7, 59-66 (1988)] of the existence of periodic solutions of third order differential equations with delay, the author examines here the specific issue of the existence of resonant and nonresonant oscillations of equations of the form \(\dddot x (t)+f(\dot x(t)) \ddot x(t)+g(t,\dot x(t-\tau)) + h(x(t))=p(t)\) in which \(\tau \in [0,2 \pi)\) is a fixed delay. Here \(f,h:R \to R\) are continuous, \(g:[0,2\pi] \times R \to R\) is Carathéodory, \(p \in L^ 2_{2\pi}\) and both \(g\) and \(p\) are \(2 \pi\)-periodic in \(t\). The general treatment is said to be motivated by some results of J. Mawhin and J. R. Ward [Arch. Math. 41, 337-351 (1983; Zbl 0537.34037)], E. De Pascale and R. Iannacci [Equadiff. 82, Lect. Notes Math. 1017, 148-156 (1983; Zbl 0522.34064)] and the reviewer and M. N. Nkashama [Nonlinear Anal., Theory Methods Appl. 12, No. 10, 1029-1046 (1988; Zbl 0676.34021)].
For the entire collection see [Zbl 0780.00043].
For the entire collection see [Zbl 0780.00043].
Reviewer: J.O.C.Ezeilo (Nsukka)
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34C25 | Periodic solutions to ordinary differential equations |
