The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x(t)+(-1)^r P(t) x(g(t))]+\delta Q(t) f(x(h(t))) = 0,$ where $\ n \ge 2,\ r \in \lbrace 1,2\rbrace ,\ $ and $ \delta = \pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.
@article{107516,
author = {Miroslava R\r u\v zi\v ckov\'a and E. \v Sp\'anikov\'a},
title = {Oscillation theorems for neutral differential equations with the quasi-derivatives},
journal = {Archivum Mathematicum},
volume = {030},
year = {1994},
pages = {293-300},
zbl = {0819.34046},
mrnumber = {1322574},
language = {en},
url = {http://dml.mathdoc.fr/item/107516}
}
Růžičková, Miroslava; Špániková, E. Oscillation theorems for neutral differential equations with the quasi-derivatives. Archivum Mathematicum, Tome 030 (1994) pp. 293-300. http://gdmltest.u-ga.fr/item/107516/
On the oscillation of an $n$th-order nonlinear neutral delay differential equation, J. Comp. Appl. Math. 41 (1992), 35-40. (1992) | MR 1181706
Oscillation properties of first order nonlinear functional differential equations of neutral type, Diff. and Int. Equat. (1991), 425-436. (1991) | MR 1081192
Oscillatory properties of functional differential systems of neutral type, Czech. Math. J. 43 (1993), 649-662. (1993) | MR 1258427
Nonoscillatory solutions of differential equations with deviating argument, Czech. Math. J. 36 (111) (1986), 93-107. (1986) | MR 0822871
Oscillation of bounded solutions of neutral differential equations, Appl. Math. Lett. 2 (1993), 43-46. (1993) | MR 1347773