Oscillation of first order linear differential equations with several non-monotone delays

Abstract

Consider the rst-order linear di erential equation with several retarded argumentswhere the functions, τ k (t) < t for t ≥ t and lim t→∞ τ k (t) = ∞, for every k = , , . . . , n.Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

On the Oscillatory Behavior of Solutions of Second-Order Non-Linear Differential Equations with Damping Term

“…We mention here, as examples, Grace and Lalli [13], who studied the oscillatory behavior of Equation (2) using integral averaging techniques in the case r(ι) and Q(ι) are not assumed to be non-negative for all values of ι. In [14], Grace established new oscillation results in the spirit of those obtained by Kamenev, Philos, and Yan for a broad class of second-order nonlinear equations of Type (2). In [25], Tiryaki and Zafer made use of Philos's technique [20] to establish new oscillation criteria for Equation (2) in the case where P(ι) and Q(ι) are allowed to change signs on [ι 0 , ∞).…”

“…Their criteria cover new classes of equations discussed by the authors in [11,13,14,27]. In [22], S. Rogovchenko and Yuri Rogovchenko discussed the oscillatory behavior for different second-order equations like (2) and some equations more general than (2). Moreover, in [23], Rogovchenko and Tuncay used the averaging technique and strengthened the results of Kirane and Rogovchenko [16], Grace [14], Philos [20], and Yan [27].…”

“…Jiang et al [15] discussed a class of equations more general than (1) and ( 2), where they employed the generalized Riccati transformation and a class of functions to establish several oscillation criteria for monotonic and non-monotonic functions to improve some results obtained in the literature. In [26], Wang and Song studied a class of second-order nonlinear differential equations with a damping term which is more general than (1) and (2). They established some new sufficient conditions by using the refined integral averaging technique.…”

A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

“…In 2018 Attia et al [24] established the following oscillation conditions under the assumption that there exists a family of nondecreasing continuous functions g i (t), i = 1, 2, ..., m and a nondecreasing continuous functions g(t) such that for some t 1 ≥ t 0…”

New Explicit Oscillation Criteria for First-Order Differential Equations with Several Non-Monotone Delays

“…In the last few decades, the oscillation problem of functional differential equations has received much attention from mathematicians; see, for example, . The reader is referred to [1,2,[4][5][6]9,10,12,13,17,20,22,23,26] and [1,2,7,8,11,14,15,[17][18][19]24,27,[30][31][32][34][35][36][37] for the oscillation of Equations ( 1) and (2), respectively. The results on oscillation criteria of most of these works have iterative forms.…”