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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 $\underset{t \to \infty}{lim inf} | x (t) | = 0 .$

Necessary and sufficient conditions for oscillation of delay equations with constant coefficients

Myron K. Grammatikopoulos; Gerasimos Ladas; Yiannis G. Sficas — 1987

Czechoslovak Mathematical Journal

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Minimal and maximal solutions for two-point boundary-value problems.

Perturbed Fredholm boundary value problems for delay differential systems.

On the singularities of 3-D Protter's problem for the wave equation.

On the positive solutions of a higher order functional differential equation with a discontinuity.

О колеблемости ограниченных решений дифференциальных уравнений с возмущёнными аргументами

Nonoscillation theorems for functional differential equations of arbitrary order.

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

Necessary and sufficient conditions for oscillation of delay equations with constant coefficients