Displaying similar documents to “On solutions of linear difference equations with infinite delay.”

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.

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.

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.

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...

Existence results for delay second order differential inclusions

Dalila Azzam-Laouir, Tahar Haddad (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.

Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments

Srinivasan Selvarangam, Sethurajan A. Rupadevi, Ethiraju Thandapani, Sandra Pinelas (2021)

Mathematica Bohemica

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In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation Δ 3 ( x n + a n x n - l + b n x n + m ) + p n x n - k - q n x n + r = 0 , n ≥ n 0 via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing results.

On a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems

Ch. G. Philos (2007)

Annales Polonici Mathematici

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This article is concerned with a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems. By the use of the Schauder-Tikhonov theorem, a result on the existence of solutions is obtained. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of solutions is established. Moreover, these results are applied to the special case of ordinary differential systems and to a certain class of delay differential...