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Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations ${(- 1)}^{m + 1} \frac{d^{m} y_{i} (t)}{d t^{m}} + \sum_{j = 1}^{n} q_{i j} y_{j} (t - h_{j j}) = 0, m \geq 1, i = 1, 2, ..., n,$ to be oscillatory, where $q_{i j} ε (- \infty, \infty)$ , $h_{j j} \in (0, \infty)$ , $i, j = 1, 2, ..., n$ . Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations ${(- 1)}^{m + 1} \frac{d^{m}}{d t^{m}} (y_{i} (t) + c y_{i} (t - g)) + \sum_{j = 1}^{n} q_{i j} y_{j} (t - h) = 0,$ where $c$ , $g$ and $h$ are real constants and $i = 1, 2, ..., n$ .

Oscillations of functional differential equations.

Stavroulakis, I.P. (1997)

Memoirs on Differential Equations and Mathematical Physics

Oscillations of higher order differential equations of neutral type

N. Parhi (2000)

Czechoslovak Mathematical Journal

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of $n$ th order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.

Oscillations of neutral differential systems

Bozena Mihalíková (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim of this paper is to present the sufficient conditions for oscillation of solutions of the system of differential equations of neutral type.

Oscillations of second-order neutral impulsive differential equations.

Cheng, Jin-Fa, Chu, Yu-Ming (2010)

Journal of Inequalities and Applications [electronic only]

Oscillatority conditions for nonlinear systems with delay.

Efimov, Denis V., Fradkov, Alexander L. (2007)

Journal of Applied Mathematics

Oscillatory and asymptotic behaviour of a neutral differential equation with oscillating coefficients.

Dix, J.G., Misra, N., Padhy, L.N., Rath, R.N. (2008)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

Radhanath N. Rath, Niyati Misra, Laxmi N. Padhy (2007)

Mathematica Slovaca

Oscillatory and nonoscillatory solutions of neutral differential equations

Satoshi Tanaka (2000)

Annales Polonici Mathematici

Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.

Oscillatory behavior of quasilinear neutral delay dynamic equations on time scales.

Han, Zhenlai, Sun, Shurong, Li, Tongxing, Zhang, Chenghui (2010)

Advances in Difference Equations [electronic only]

Oscillatory behaviour of a higher order nonlinear neutral delay type functional differential equation with oscillating coefficients

Yaşar Bolat, Ömer Akin (2005)

Czechoslovak Mathematical Journal

In this paper we are concerned with the oscillation of solutions of a certain more general higher order nonlinear neutral type functional differential equation with oscillating coefficients. We obtain two sufficient criteria for oscillatory behaviour of its solutions.

Oscillatory behaviour of certain difference equations

Said R. Grace (2000)

Mathematica Slovaca

Oscillatory behaviour of solutions of forced neutral differential equations

N. Parhi, P. K. Mohanty (1996)

Annales Polonici Mathematici

Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.

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Displaying 141 – 160 of 162

Oscillation theorems for second-order forced neutral nonlinear differential equations with delayed argument.

Oscillation theorems of comparison type for neutral nonlinear functional differential equations

Oscillations and nonoscillations in retarded equations.

Oscillations of certain delay integro-differential equations.

Oscillations of certain functional differential equations