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A comparison theorem for linear delay differential equations

Jozef Džurina (1995)

Archivum Mathematicum

In this paper property (A) of the linear delay differential equation L n u ( t ) + p ( t ) u ( τ ( t ) ) = 0 , is to deduce from the oscillation of a set of the first order delay differential equations.

About differential inequalities for nonlocal boundary value problems with impulsive delay equations

Alexander Domoshnitsky, Irina Volinsky (2015)

Mathematica Bohemica

We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the...

Asymptotic and exponential decay in mean square for delay geometric Brownian motion

Jan Haškovec (2022)

Applications of Mathematics

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of asymptotic decay. For exponential decay, they are easily resolvable numerically. The analytical method is based on construction of a Lyapunov functional (asymptotic decay) and a forward-backward estimate for the square mean (exponential decay).

Asymptotic behavior of solutions of third order delay differential equations

Mariella Cecchi, Zuzana Došlá (1997)

Archivum Mathematicum

We give an equivalence criterion on property A and property B for delay third order linear differential equations. We also give comparison results on properties A and B between linear and nonlinear equations, whereby we only suppose that nonlinearity has superlinear growth near infinity.

Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments

Roman Koplatadze, N. L. Partsvania, Ioannis P. Stavroulakis (2003)

Archivum Mathematicum

Sufficient conditions are established for the oscillation of proper solutions of the system u 1 ' ( t ) = p ( t ) u 2 ( σ ( t ) ) , u 2 ' ( t ) = - q ( t ) u 1 ( τ ( t ) ) , where p , q : R + R + are locally summable functions, while τ and σ : R + R + are continuous and continuously differentiable functions, respectively, and lim t + τ ( t ) = + , lim t + σ ( t ) = + .

Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type

Takaŝi Kusano, Pavol Marušiak (2000)

Mathematica Bohemica

This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as t .

Asymptotic properties of third order functional dynamic equations on time scales

I. Kubiaczyk, S. H. Saker (2011)

Annales Polonici Mathematici

The purpose of this paper is to study the asymptotic properties of nonoscillatory solutions of the third order nonlinear functional dynamic equation [ p ( t ) [ ( r ( t ) x Δ ( t ) ) Δ ] γ ] Δ + q ( t ) f ( x ( τ ( t ) ) ) = 0 , t ≥ t₀, on a time scale , where γ > 0 is a quotient of odd positive integers, and p, q, r and τ are positive right-dense continuous functions defined on . We classify the nonoscillatory solutions into certain classes C i , i = 0,1,2,3, according to the sign of the Δ-quasi-derivatives and obtain sufficient conditions in order that C i = . Also, we establish...

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