This paper deals with the second order nonlinear neutral differential inequalities $(A_\nu )$: $(-1)^\nu x(t)\,\lbrace \,z^{\prime \prime }(t)+(-1)^\nu q(t)\,f(x(h(t))) \rbrace \le 0,\ $ $t\ge t_0\ge 0,$ where $\ \nu =0\ $ or $\ \nu =1,\ $ $\ z(t)\,=\,x(t)\,+\,p(t)\,x(t-\tau ),\ $ $\ 0<\tau =\ $ const, $\ p,q,h:[t_0,\infty )\rightarrow R\ $ $\ f:R\rightarrow R\ $ are continuous functions. There are proved sufficient conditions under which every bounded solution of $(A_\nu )$ is either oscillatory or $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.$
@article{107521,
author = {Myron K. Grammatikopoulos and Pavol Maru\v siak},
title = {Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients},
journal = {Archivum Mathematicum},
volume = {031},
year = {1995},
pages = {29-36},
zbl = {0832.34066},
mrnumber = {1342372},
language = {en},
url = {http://dml.mathdoc.fr/item/107521}
}
Grammatikopoulos, Myron K.; Marušiak, Pavol. Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients. Archivum Mathematicum, Tome 031 (1995) pp. 29-36. http://gdmltest.u-ga.fr/item/107521/
Oscillation Theory for Neutral Equations with Delay, Adam Hilger IOP Pablisching Ltd. (1991) 288pp..
Oscillation and asymptotic behavior of second order neutral differential equations with deviating arguments, Canad. Math. Soc. V8 (1967) 153$-$161. | MR 0909906
Asymptotic Properties of Solutions of Neutral Delay Differential Equations of the Second Order, Radovi Matematički $\ V_4\ $ (1988) 113 $-$149.
On the Asymptitic Behavior of Solutions of Second Order Nonlinear Neutral Delay Differential Equations,, Journal Math. Anal. Appl. V156 $N_1$ (1991) 23$-$39. | MR 1102594
Asymptotic Behavior of Nonoscillatory Solutions of Neutral Delay Differential Equations of Arbitrary Order, Nonlinear Analysis, Theory, Math., Appl. V21, N1 (1993) 23$-$42. | MR 1231526
Oscillation Theory of Delay Differential Equations, Clear. Press., Oxford (1991) 368pp. | MR 1168471
Sufficient conditions for oscillations of higher order linear functional differential equations of neutral type, Japan J. Math.15 (1989) 415$-$432. | MR 1039249
Oscillation properties of first order nonlinear functional differential equations of neutral type, Diff. and Int. Equat. (1991) 425$-$436. | MR 1081192
Nonoscillation theorems for differential equation with deviating argument, Pacific J. Math. 63, $N_1$ (1976) 185$-$192. | MR 0417536