Displaying similar documents to “Applications of Characteristic Equation of Linear Delay Difference Equations”

Oscillation of delay differential equations

J. Džurina (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.

Characterization of shadowing for linear autonomous delay differential equations

Mihály Pituk, John Ioannis Stavroulakis (2025)

Czechoslovak Mathematical Journal

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A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.

On oscillation of a kind of integro-differential equation with delay

Binggen Zhang (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This note contains a criterion for the oscillation of solution of a kind of integro-differential equations with delay.

Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms

George E. Chatzarakis, Ponnuraj Dinakar, Srinivasan Selvarangam, Ethiraju Thandapani (2022)

Mathematica Bohemica

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We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known...

On the behavior of the solutions to autonomous linear difference equations with continuous variable

Christos G. Philos, Ioannis K. Purnaras (2007)

Archivum Mathematicum

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Autonomous linear neutral delay and, especially, (non-neutral) delay difference equations with continuous variable are considered, and some new results on the behavior of the solutions are established. The results are obtained by the use of appropriate positive roots of the corresponding characteristic equation.

Oscillation of Nonlinear Neutral Delay Differential Equations

Elabbasy, E. M., Hassan, T. S. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 34K15, 34C10. In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation (x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0, where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example.