scholarly journals On exponential stability of a linear delay differential equation with an oscillating coefficient

2009 ◽  
Vol 22 (12) ◽  
pp. 1833-1837 ◽  
Author(s):  
Leonid Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Linear Delay ◽  
Oscillating Coefficient ◽  
Delay Differential

scholarly journals New Stability Conditions for Linear Differential Equations with Several Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Leonid Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Linear Differential Equations ◽  
Stability Conditions ◽  
Linear Delay ◽  
Linear Differential ◽  
Several Delays ◽  
Delay Differential

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equationx˙(t)+∑k=1mak(t)x(hk(t))=0with measurable delays and coefficients. These results are compared to known stability tests.

ON STABILITY OF THE SECOND ORDER DELAY DIFFERENTIAL EQUATION: THREE METHODS

2021 ◽  
Vol 28 (1-2) ◽  
pp. 3-17
Author(s):  
LEONID BEREZANSKY
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Second Order ◽  
Operator Equations ◽  
Linear Delay ◽  
Delay Differential

The aim of the paper is a review of some methods on exponential stability for linear delay differential equations of the second order. All these methods are based on Bohl-Perron theorem which reduces stability investi-gations to study the properties of operator equations in some functional spaces. As an example of application of these methods we consider the following equation x¨(t)+ a(t)˙x(g(t)) + b(t)x(h(t)) = 0.

Exponential stability of a second order delay differential equation without damping term

2015 ◽  
Vol 258 ◽  
pp. 483-488 ◽  
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Mikhail Gitman ◽  
Valery Stolbov
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Second Order ◽  
Damping Term ◽  
Delay Differential

Nonoscillation and exponential stability of the second order delay differential equation with damping

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Mikhail Gitman ◽  
Valery Stolbov
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Second Order ◽  
Delay Differential

AbstractFor a delay differential equation

scholarly journals New Oscillation and Nonoscillation Criteria for a Class of Linear Delay Differential Equation

2019 ◽  
Vol 8 (10) ◽  
pp. 308-313
Keyword(s):  
Differential Equation ◽  
Continuous Function ◽  
Delay Differential Equation ◽  
Sufficient Condition ◽  
First Order ◽  
Linear Delay ◽  
Piecewise Continuous ◽  
Delay Differential ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

In this article the authors established sufficient condition for the first order delay differential equation in the form , ( ) where , = and is a non negative piecewise continuous function. Some interesting examples are provided to illustrate the results. Keywords: Oscillation, delay differential equation and bounded. AMS Subject Classification 2010: 39A10 and 39A12.

scholarly journals Steklov problem of the first class for a fractional order delay differential equation

2021 ◽  
pp. 30-37
Author(s):  
М.Г. Мажгихова
Keyword(s):  
Differential Equation ◽  
Green Function ◽  
Delay Differential Equation ◽  
Existence And Uniqueness ◽  
Function Method ◽  
Existence And Uniqueness Theorem ◽  
Green Function Method ◽  
Steklov Problem ◽  
Linear Delay ◽  
Delay Differential

Методом функции Грина получено решение задачи Стеклова первого класса для линейного уравнения с дробной производной Герасимова-Капуто с запаздывающим аргументом. Доказана теорема существования и единственности задачи. The solution to the Steklov problem with conditions of the first class for a linear delay differential equation with a Gerasimov-Caputo fractional derivative is obtained by Green function method. The existence and uniqueness theorem to the problem is proved.

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