On oscillation of nonlinear delay differential equations

Abstract

Abstract. Necessary, sufficient, and necessary and sufficient conditions are obtained for all solutions of the nonlinear differential equation Our results show that for a certain class of nonlinear functions /, (*) oscillates if and only if (**) oscillates. As an application of our results, we obtain simple sufficient and necessary and sufficient conditions for the oscillation of several nonlinear delay differential equations which appear in applications.

Asymptotic behavior and oscillation of functional differential equations

“…Remark. Under additional sign conditions on the coefficients of (4.1), the conclusion of the corollary was obtained by Kulenovic et al [11] (see also [5,Theorem 1.5.1] Remark. In contrast to the autonomous case (4.4), the converse of Corollary 4.3 in general is not true.…”

Oscillation and nonoscillation in a nonautonomous delay-logistic equation

“…-IT = n a -> b,u(t -t,) 7=1 (1.2) where a, bj, (j = 1,2 n) are positive constants has been recently discussed by Gopalsamy [2] and Kulenovic et al [6]. The literature on oscillation of scalar systems with deviating arguments is quite extensive and we refer to the books by Shevelo [8] and Lakshmikantham et al [7] for more details.…”

A comparison result for the oscillation of delay differential equations

“…It also extends and improves in a certain way Theorems 2 and 5 of [4] which for the sake of comparison we summarize below. Remark 1.…”