Comparison theorems for functional differential equations with deviating arguments

Oscillation of strongly noncanonical equations

“…There are numerous papers dealing with oscillatory properties of (E) (see, e.g., [1][2][3][4][5][6][7][8]10]). Most papers are devoted to canonical equations, where conditions opposite to (1.1) are assumed to hold, that is,…”

Property (A) of third-order advanced differential equations

“…This comparison theorem has been generalized by Kusano and Naito [14] and Dzurina [7] to differential equations with quasi-derivatives. But the corresponding comparison principle for advanced differential equations is still missing.…”

“…Following Foster and Grimmer [10] and Kusano and Naito [14], we say that x(t) is a solution of degree 0 if it satisfies (C 0 ), while x(t) satisfying (C 2 ) is said to be of degree 2. If we denote by N the set of all nonoscillatory solution of degree , then the set N of all nonoscillatory solutions of (E) has the following decomposition N = N 0 ∪ N 2 .…”

Asymptotic properties of the third order delay differential equations

“…In a recent paper [3] Kusano and Naito have presented a useful comparison principle which under conditions (i) and (ii) enables us to deduce property (B) of a delay equation of the form (1) from that of the ordinary differential equation…”