scholarly journals On the Periodicity of General Class of Difference Equations

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 75 ◽  
Author(s):  
Osama Moaaz ◽  
Hamida Mahjoub ◽  
Ali Muhib
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Usual Method ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient

In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.

PERIODIC SOLUTIONS OF FORCED OSCILLATORS WITH SEVERAL DEGREES OF FREEDOM

2002 ◽  
Vol 34 (3) ◽  
pp. 308-318 ◽  
Author(s):  
RAFAEL ORTEGA ◽  
LUIS A. SÁNCHEZ
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Forced Oscillators ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient ◽  
New Phenomena

Results of the Landesman–Lazer type provide necessary and sufficient conditions for the existence of periodic solutions of certain nonlinear differential equations with forcing. Typically, they deal with scalar problems. This paper presents a discussion of possible extensions to systems. The emphasis is placed on the new phenomena produced by the increase of the dimension.

scholarly journals A Note on the Periodic Solutions for a Class of Third Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 31
Author(s):  
Zouhair Diab ◽  
Juan L. G. Guirao ◽  
Juan A. Vera
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Monodromy Matrix ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Averaging Theory ◽  
Third Order ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Necessary And Sufficient

The aim of the present work is to study the necessary and sufficient conditions for the existence of periodic solutions for a class of third order differential equations by using the averaging theory. Moreover, we use the symmetry of the Monodromy matrix to study the stability of these solutions.

scholarly journals Some Qualitative Behavior of Solutions of General Class of Difference Equations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 585 ◽  
Author(s):  
Osama Moaaz ◽  
Dimplekumar Chalishajar ◽  
Omar Bazighifan
Keyword(s):  
Periodic Solution ◽  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Qualitative Behavior ◽  
Local Asymptotic Stability ◽  
Necessary And Sufficient

In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

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