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Featured researches published by Leonid Berezansky.


Archive | 2012

Nonoscillation Theory of Functional Differential Equations with Applications

Ravi P. Agarwal; Leonid Berezansky; Elena Braverman; Alexander Domoshnitsky

1. Introduction to Oscillation Theory.- 2. Scalar Delay Differential Equations on Semiaxes.- 3. Scalar Delay Differential Equations on Semiaxis with Positive and Negative Coefficients.- 4. Oscillation of Equations with a Distributed Delay.- 5. Scalar Advanced and Mixed Differential Equations on Semiaxes.- 6. Neutral Differential Equations.- 7. Second Order Delay Differential Equations.- 8. Second Order Delay Differential Equations with Damping Terms.- 9. Vector Delay Differential Equations.- 10. Linearized Methods for Nonlinear Equations with a Distributed Delay.- 11. Nonlinear Models - Modifications of Delay Logistic Equations.- 12. First Order Linear Delay Impulsive Differential Equation.- 13. Second Order Linear Delay Impulsive Differential Equations.- 14. Linearized Oscillation Theory for Nonlinear Delay Impulsive Equations.- 15. Maximum Principles and Nonoscillation Intervals for First Order Volterra Functional Differential Equations.- 16. Systems of Functional Differential Equations on Finite Intervals.- 17. Nonoscillation Interval for n-th Order Functional Differential Equations.- Appendix A.- Appendix B.


Journal of Difference Equations and Applications | 2004

On Impulsive Beverton-Holt Difference Equations and their Applications

Leonid Berezansky; Elena Braverman

The asymptotic properties of the impulsive Beverton-Holt difference equation where p is a fixed positive integer, are considered. The results are applied to an impulsive logistic equation with non-constant coefficients In particular, sufficient extinction and non-extinction conditions are obtained for both equations.


Journal of Difference Equations and Applications | 2005

Sufficient conditions for the global stability of nonautonomous higher order difference equations

Leonid Berezansky; Elena Braverman; Eduardo Liz

We present some explicit sufficient conditions for the global stability of the zero solution in nonautonomous higher order difference equations. The linear case is discussed in detail. We illustrate our main results with some examples. In particular, the stability properties of the equilibrium in a nonlinear model in macroeconomics is addressed.


Applied Mathematics Letters | 2009

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

Leonid Berezansky; Elena Braverman

Abstract New explicit exponential stability conditions are obtained for the nonautonomous linear equation x ( t ) + a ( t ) x ( h ( t ) ) = 0 , where h ( t ) ≤ t and a ( t ) is an oscillating function. We apply the comparison method based on the Bohl–Perron type theorem. Coefficients and delays are not assumed to be continuous. Some real-world applications and several examples are also discussed.


Abstract and Applied Analysis | 2010

On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays

Jaromír Baštinec; Leonid Berezansky; Josef Diblík; Zdeněk Šmarda

New nonoscillation and oscillation criteria are derived for scalar delay differential equations 𝑥(𝑡)


Journal of Mathematical Analysis and Applications | 2002

On oscillation properties of delay differential equations with positive and negative coefficients

Leonid Berezansky; Yury Domshlak; Elena Braverman

Abstract For a scalar delay differential equation x (t)+a(t)x h(t) −b(t)x g(t) =0, a(t)⩾0, b(t)⩾0, h(t)⩽t, g(t)⩽t, a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequalities, positiveness of the fundamental function and existence of a nonnegative solution for a certain explicitly constructed nonlinear integral inequality. A comparison theorem and explicit nonoscillation and oscillation results are presented.


Zeitschrift Fur Analysis Und Ihre Anwendungen | 2001

Oscillation of Equations with Distributed Delays

Ravi P. Agarwal; Leonid Berezansky; Elena Braverman; Alexander Domoshnitsky

Chapter 4 deals with nonoscillation properties of scalar linear differential equations with a distributed delay. It is usually believed that equations with a distributed delay, which involve differential equations with several variable delays, integrodifferential equations and mixed equations with concentrated delays and integral terms, provide a more realistic description for models of population dynamics and mathematical biology in general.


Abstract and Applied Analysis | 2011

A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δ()=−()(−) with a Positive Coefficient

Jaromír Baštinec; Leonid Berezansky; Josef Diblík; Zdenĕk Šmarda

A linear ( 𝑘 + 1 ) th-order discrete delayed equation Δ 𝑥 ( 𝑛 ) = − 𝑝 ( 𝑛 ) 𝑥 ( 𝑛 − 𝑘 ) where 𝑝 ( 𝑛 ) a positive sequence is considered for 𝑛 → ∞ . This equation is known to have a positive solution if the sequence 𝑝 ( 𝑛 ) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for 𝑝 ( 𝑛 ) , all solutions of the equation considered are oscillating for 𝑛 → ∞ .


Journal of Computational and Applied Mathematics | 2000

On oscillation of a logistic equation with several delays

Leonid Berezansky; Elena Braverman

Abstract For a scalar delay logistic equation y (t)=y(t) ∑ k=1 m r k (t) 1− y(h k (t)) K , h k (t)⩽t, a connection between oscillating properties of this equation, the corresponding differential inequalities and the linear equation x (t)+ ∑ k=1 m r k (t)x(h k (t))=0, is established. Explicit nonoscillation and oscillation conditions are presented.


Abstract and Applied Analysis | 2011

New Stability Conditions for Linear Differential Equations with Several Delays

Leonid Berezansky; Elena Braverman

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation ∑𝑥(𝑡)

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Lev Idels

Vancouver Island University

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Josef Diblík

Brno University of Technology

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Yury Domshlak

Ben-Gurion University of the Negev

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Zdeněk Šmarda

Central European Institute of Technology

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Jaromír Baštinec

Brno University of Technology

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Zdeněk Svoboda

Central European Institute of Technology

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Zdenĕk Šmarda

Brno University of Technology

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