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W-transform for exponential stability of second order delay differential equations without damping terms

In this paper a method for studying stability of the equation x ″ ( t ) + ∑ i = 1 m a i ( t ) x ( t − τ i ( t ) ) = 0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x ″ ( t ) + ∑ i = 1 m a i ( t ) x ( t ) = 0 is not exponentially stable, the delay equation can be exponentially stable. MSC: ...

Nonoscillation, maximum principles, and exponential stability of second order delay differential equations without damping term

Delays, arising in nonoscillatory and stable ordinary differential equations, can induce oscillation and instability of their solutions. That is why the traditional direction in the study of nonoscillation and stability of delay equations is to establish a smallness of delay, allowing delay differential equations to preserve these convenient properties of ordinary differential ...

About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations

Domoshnitsky 0 0 Department of Mathematics and Computer Sciences, Ariel University of Samaria , Ariel , Israel The purpose of this paper is to propose a method for studying integro-differential equations with

About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations

Yakov Goltser 0 Alexander Domoshnitsky 0 0 Department of Mathematics and Computer Sciences, Ariel University of Samaria , Ariel , Israel The purpose of this paper is to propose a method for studying

Stability and estimate of solution to uncertain neutral delay systems

The coefficients and delays in models describing various processes are usually obtained as a results of measurements and can be obtained only approximately. We deal with the question of how to estimate the influence of ‘mistakes’ in coefficients and delays on solutions’ behavior of the delay differential neutral system ...

Differential Inequalities for One Component of Solution Vector for Systems of Linear Functional Differential Equations

Alexander Domoshnitsky 0 0 Department of Mathematics and Computer Science, The Ariel University Center of Samaria , 44837 Ariel , Israel The method to compare only one component of the solution

A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia

Domoshnitsky 0 0 Department of Computer Science and Mathematics, Ariel University Center of Samaria , Ariel, 40700 , Israel In this paper, we propose and analyze a mathematical model for the treatment of

A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia

In this paper, we propose and analyze a mathematical model for the treatment of chronic myelogenous (myeloid) leukemia (CML), a cancer of the blood. Our main focus is on the combined treatment of CML based on imatinib therapy and immunotherapy. Treatment with imatinib is a molecular targeted therapy that inhibits the cells involved in the chronic CML pathogenesis. Immunotherapy ...

Component-wise positivity of solutions to periodic boundary problem for linear functional differential system

The classical Ważewski theorem claims that the condition pij ≤ 0, j ≠ i, i, j =1,...,n, is necessary and sufficient for non-negativity of all the components of solution vector to a system of the inequalities x ′ ( t ) + ∑ j = 1 n p i j ( t ) x ( t ) ≥ 0 , xi (0) ≥ 0, i =1, ..., n. Although this result was extent on various boundary value problems and on delay differential systems, ...

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

. Alexander Domoshnitsky: Department of Mathematics and Computer Sciences, The Academic College of Judea and Samaria, Ariel 44837, Israel Email address: [1] T. A. Chanturiya , “ Specific conditions for the

Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

Domoshnitsky 0 Abraham Maghakyan 0 Roman Shklyar 0 Recommended by Marta A D Garc´ıa-Huidobro 0 Department of Mathematics and Computer Science, Ariel University Center of Samaria , Ariel 44837 , Israel We obtain