Oscillation in Differential Equations with Positive and Negative Coefficients

Abstract

We obtain sufficient conditions for the oscillation of all solutions of the linear delay differential equation with positive and negative coefficientswhereExtensions to neutral differential equations and some applications to the global asymptotic stability of the trivial solution are also given.

Oscillation of Systems of Neutral Equations with Variable Coefficients

“…When n = 1, system (1) under the hypothesis (H) reduces to a scalar neutral delay differential equation with positive and negative coefficients whose oscillatory behavior has been investigated in [2], [3] and [7]. In this paper we study the oscillation of systems of the form (l), (2) and we illustrate our results which substantially improve some known results for the scalar case.…”

“…When n = 1 and R(t) 3 0, Eq. (1) with hypothesis (H) reduces to a scalar differential [7]. The detail is omitted for the lack of the space.…”

Necessary and sufficient conditions on asymptotic behaviour of solutions of forced neutral delay dynamic equations

“…First, we show that Γ x + Ψ y ∈ Ω for all x, y ∈ Ω. In fact, in view of (16), for all x, y ∈ Ω and all t ∈ [t 2 , ∞) T , we have…”

“…is studied extensively, the readers can find some results in [15][16][17][18][19] with linear delays of slope 1, except [20].…”

Oscillation of first order delay differential equations

“…Integral conditions like (3) have been employed by many authors in the study of the oscillatory properties of various functional differential equations. For example, see papers by Grammatikopoulos, Grove and Ladas [7], by Ladas and Qian [11], and by Zhang and Gopalsamy [10].…”