R. Koplatadze

On the oscillation of solutions of first-order delay differential inequalities and equations

Oscillation criteria generalizing a series of earlier results are established for first-order linear delay differential inequalities and equations.

Properties A and B of nth Order Linear Differential Equations with Deviating Argument

AbstractSufficient conditions for the nth order linear differential equation n

Quasi-linear functional differential equations with Property A

u^{(n)} (t) + p(t)u(r(t)) = 0,{text{ }}n geqslant 2

On the Kneser-Type Solutions for Two-Dimensional Linear Differential Systems with Deviating Arguments

n, to have Property A or Property B are established in both the delayed and the advanced cases. These conditions essentially improve many known results not only for differential equations with deviating arguments but for ordinary differential equations as well.

Specific properties of solutions of first order differential equations with several delay arguments

In the paper the general linear functional differential equation with several distributed deviations is considered. Sufficient conditions for the equation to have Property A (see Definition 1.2 below) are established. The obtained results are new even for Eq. (1.4).

On Asymptotic Behavior of Solutions of Generalized Emden-Fowler Differential Equations with Delay Argument

Abstract We study oscillatory properties of solutions of a functional differential equation of the form (0.1) u ( n ) ( t ) + F ( u ) ( t ) = 0 , where n ⩾ 2 and F : C ( R + ; R ) → L loc ( R + ; R ) is a continuous mapping. Sufficient conditions are established for this equation to have the so-called Property A. The obtained results are also new for the generalized Emden–Fowler type ordinary differential equation. The method by which the oscillatory properties of Eq. (0.1) are established enables one to obtain optimal conditions for (0.1) to have Property A for sufficiently general equations (for some classes of functions the obtained sufficient conditions are necessary as well).

Oscillation criteria of first order linear difference equations with delay argument

Abstract We study oscillatory properties of solutions of a functional differential equation of the form 𝑢(𝑛)(𝑡) + 𝐹(𝑢)(𝑡) = 0, where 𝑛 ≥ 2 and 𝐹 : 𝐶(𝑅+; 𝑅) → 𝐿 loc (𝑅+; 𝑅) is a continuous mapping. Sufficient conditions for this equation to have the so-called Property A are established. In the case of ordinary differential equation the obtained results lead to an integral generalization of the well-known theorem by Kondratev.

Optimal oscillation criteria for first order difference equations with delay argument

For the differential system,,, where,,, we get necessary and sufficient conditions that this system does not have solutions satisfying the condition for. Note one of our results obtained for this system with constant coefficients and delays (, where and). The inequality is necessary and sufficient for nonexistence of solutions satisfying this condition.