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.

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 Periodic solutions of Lienard differential equations via averaging theory of order two

2015 ◽  
Vol 87 (4) ◽  
pp. 1905-1913
Author(s):  
JAUME LLIBRE ◽  
DOUGLAS D. NOVAES ◽  
MARCO A. TEIXEIRA
Keyword(s):  
Positive Integer ◽  
Differential Equations ◽  
Periodic Function ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Second Order ◽  
Averaging Theory ◽  
Existence Of Periodic Solutions

Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ( x ) x ′ + n 2 x + g ( x ) = ε 2 p 1 ( t ) + ε 3 p 2 ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.

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.

scholarly journals On nonoscillatory solutions tending to zero of third-order nonlinear differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Ivan Mojsej ◽  
Alena Tartal’ová
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
The Third ◽  
Necessary And Sufficient

Abstract The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.

scholarly journals Oscillation Criteria of Solutions of Third Order Neutral Integro-Differential Equations

2021 ◽  
pp. 3642-3647
Author(s):  
Taghreed Hussein Abed ◽  
Sattar Naser Ketab ◽  
Hussain Ali Mohamad
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Necessary And Sufficient

      Some necessary and sufficient conditions are obtained that guarantee the oscillation of all solutions of two types of neutral integro-differential equations of third order. The integral is used in the sense of Riemann-Stieltjes. Some examples were included to illustrate the obtained results

scholarly journals Nonoscillation of the solutions of impulsive differential equations of third order

2001 ◽  
Vol 14 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Margarita Boneva Dimitrova
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Nonoscillatory Solution ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Impulse Effect ◽  
Necessary And Sufficient

Necessary and sufficient conditions are found for existence of at least one bounded nonoscillatory solution of a class of impulsive differential equations of third order and fixed moments of impulse effect. Some asymptotic properties of the nonoscillating solutions are investigated.

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