EUDML

This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as $t \to \infty$ .

Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients

Myron K. Grammatikopoulos; Pavol Marušiak — 1995

Archivum Mathematicum

This paper deals with the second order nonlinear neutral differential inequalities $(A_{ν})$ : ${(- 1)}^{ν} x (t) {z^{''} (t) + {(- 1)}^{ν} q (t) f (x (h (t)))} \leq 0,$ $t \geq t_{0} \geq 0,$ where $ν = 0$ or $ν = 1,$ $z (t) = x (t) + p (t) x (t - τ),$ $0 < τ =$ const, $p, q, h : [t_{0}, \infty) \to R$ $f : R \to R$ are continuous functions. There are proved sufficient conditions under which every bounded solution of $(A_{ν})$ is either oscillatory or $\underset{t \to \infty}{lim inf} | x (t) | = 0 .$

On the relation between boundedness and oscillation of solutions of many-dimensional differential systems with deviating arguments

Pavol Marušiak; Vladimir Nikolajevič Shevelo — 1987

Czechoslovak Mathematical Journal

Asymptotic properties of solutions of functional differential systems

Anatolij F. Ivanov; Pavol Marušiak — 1992

Mathematica Bohemica

In the paper we study the existence of nonoscillatory solutions of the system $x_{i}^{(n)} (t) = \sum_{j = 1}^{2} p_{i j} (t) f_{i j} (x_{j} (h_{i j} (t))), n \geq 2, i = 1, 2$ , with the property $l i m_{t \to \infty} x_{i} (t) / t^{k_{i}} = c o n s t \neq 0$ for some $k_{i} \in {1, 2, ..., n - 1}, i = 1, 2$ . Sufficient conditions for the oscillation of solutions of the system are also proved.

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Asymptotic properties of nonoscillatory solutions of neutral delay differential equations of $n$ -th order

Oscillatory properties of functional differential systems of neutral type

Oscillatory properties of solutions of nonlinear differential systems with deviating arguments

Some results on the oscillatory and asymptotic behavior of solutions of nonlinear delay differential inequalities

On oscillation of solutions of differential inequalities with retarded argument

Oscillation of solutions of the delay differential equation $y^{(2 n)} (t) + \sum_{i = 1}^{m} p_{i} (t) f_{j} (y [h_{i} (t)]) = 0$ , $n \geq 1$

Oscillation of solutions of delay differential equations

Дифференциальное чравнение с западывающим аргументом асимптотически эквивалентное с уравнением $y^{(n)}$ = 0

Oscillation of Solutions of Nonlinear Delay Differential Equations

Asymptotické vlastnosti riešení diferenciálnej rovnice $y^{'''} (t) + 2 A (t) y^{'} (t) + B (t) y (t) - C (t) y (t - h (t)) = 0$

On the oscillation of nonlinear differential systems with retarded arguments

On unbounded nonoscillatory solutions of systems of neutral differential equations

О колеблемости и монотонности решений нелинейных дифференвиалных уравнений с запаздывающим аргументом

Asymptotic properties of solutions of the third order quasilinear neutral differential equations

Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type

Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients

On the relation between boundedness and oscillation of solutions of many-dimensional differential systems with deviating arguments

Asymptotic properties of solutions of functional differential systems