Behaviour of solutions of linear differential equations with delay

Josef Diblík

Displaying similar documents to “Behaviour of solutions of linear differential equations with delay”

On the critical case in oscillation for differential equations with a single delay and with several delays.

Baštinec, Jaromír, Berezansky, Leonid, Diblík, Josef, Šmarda, Zdeněk (2010)

Abstract and Applied Analysis

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On the oscillation of certain class of third-order nonlinear delay differential equations

S. H. Saker, J. Džurina (2010)

Mathematica Bohemica

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In this paper we consider the third-order nonlinear delay differential equation (*) ${(a (t) {(x^{''} (t))}^{γ})}^{'} + q (t) x^{γ} (τ (t)) = 0, t \geq t_{0},$ where $a (t)$ , $q (t)$ are positive functions, $γ > 0$ is a quotient of odd positive integers and the delay function $τ (t) \leq t$ satisfies ${lim}_{t \to i n f t y} τ (t) = i n f t y$ . We establish some sufficient conditions which ensure that (*) is oscillatory or the solutions converge to zero. Our results in the nondelay case extend and improve some known results and in the delay case the results can be applied to new classes of equations which are not covered by the...

Oscillation of two delays differential equations with positive and negative coefficients.

Lakrib, Mustapha (2001)

Mathematica Pannonica

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A survey on the oscillation of solutions of first order linear differential equations with deviating arguments.

Wang, Zhicheng, Stavroulakis, Ioannis P., Qian, Xiangzheng (2002)

Applied Mathematics E-Notes [electronic only]

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Comparison theorems for the third order trinomial differential equations with delay argument

Jozef Džurina, Renáta Kotorová (2009)

Czechoslovak Mathematical Journal

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In this paper we study asymptotic properties of the third order trinomial delay differential equation $y^{'''} (t) - p (t) y^{'} (t) + g (t) y (τ (t)) = 0$ by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.