Linearized oscillations for higher order neutral differential equations. (English) Zbl 0864.34071
The linearization technique is used to study the oscillatory behaviour of a highly nonlinear equation. Some conditions are given when the oscillatory behaviour of solutions of the limiting equation predicts the oscillatory behaviour of the given nonlinear neutral differential equation.
Reviewer: S.G.Khristova (Plovdiv)
MSC:
| 34K40 | Neutral functional-differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
References:
| [1] | Arino, O.; Gyori, I., Necessary and sufficient conditions for oscillation of neutral differential systems with several delays, J. Differ. Eq., 81, 98-105 (1989) · Zbl 0691.34054 · doi:10.1016/0022-0396(89)90179-4 |
| [2] | Gopalsamy, K., Oscillatory properties of systems of first-order linear delay differential inequalities, Pac. J. Math., 128, 299-305 (1987) · Zbl 0634.34054 |
| [3] | Gopalsamy, K., Oscillations in Lotka-Volterra systems with several delays, J. Math. Anal. Appl., 159, 440-448 (1991) · Zbl 0732.34054 · doi:10.1016/0022-247X(91)90206-F |
| [4] | Gopalsamy, K., Oscillations of a system of delay logistic equations, J. Math. Anal. Appl., 146, 192-202 (1990) · Zbl 0686.34066 · doi:10.1016/0022-247X(90)90340-L |
| [5] | Kowalski, K.; Steeb, W. H., Nonlinear Dynamical Systems and Carleman Linearization (1991), Singapore: World Scientific, Singapore · Zbl 0753.34003 |
| [6] | Ladas, G.; Qian, C., Linearized oscillations for odd-order neutral delay differential equations, J. Differ. Equ., 88, 238-247 (1990) · Zbl 0717.34074 · doi:10.1016/0022-0396(90)90097-9 |
| [7] | Ladas, G.; Qian, C., Linearized oscillations for even-order neutral differential equations, J. Math. Anal. Appl., 159, 237-250 (1991) · Zbl 0729.34046 · doi:10.1016/0022-247X(91)90233-P |
| [8] | Ruan, S., Oscillations for first order neutral differential equations with variable coefficients, Bull. Aust. Math. Soc., 43, 147-152 (1991) · Zbl 0719.34135 · doi:10.1017/S0004972700028872 |
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.
