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(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman Dec 2022

(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted …


Oscillation Of Second Order Mixed Functional Differential Equations With Sublinear And Superlinear Neutral Terms, Shan Shi, Zhenlai Han Jan 2022

Oscillation Of Second Order Mixed Functional Differential Equations With Sublinear And Superlinear Neutral Terms, Shan Shi, Zhenlai Han

Turkish Journal of Mathematics

In this paper, we shall establish some new oscillation theorems for the functional differential equations with sublinear and superlinear neutral terms of the form $$ (r(t)(z'(t))^\alpha)'=q(t)x^\alpha(\tau(t)), $$ where $z(t)=x(t)+p_1(t)x^\beta(\sigma(t))-p_2(t)x^\gamma(\sigma(t))$ with $0


Oscillation Of Third-Order Neutral Differential Equations With Oscillatory Operator, Miroslav Bartusek Jan 2022

Oscillation Of Third-Order Neutral Differential Equations With Oscillatory Operator, Miroslav Bartusek

Turkish Journal of Mathematics

A third-order damped neutral sublinear differential equation for which its differential operator is oscillatory is studied. Sufficient conditions are given under which every solution is either oscillatory or the derivative of its neutral term is oscillatory (or it tends to zero).


Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie Jan 2022

Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie

Turkish Journal of Mathematics

This paper focuses on the oscillation criteria for the third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments. Using comparison principles, new sufficient conditions improve some known existing results substantially due to less constraints on the considered equation. At last, two examples are established to illustrate the given theorems.