scholarly journals CENTER PROBLEM FOR THIRD-ORDER ODEs

2013 ◽  
Vol 23 (05) ◽  
pp. 1350078 ◽  
Author(s):  
ADAM MAHDI
Keyword(s):  
Center Manifold ◽  
Sufficient Conditions ◽  
Positive Answer ◽  
Necessary And Sufficient Conditions ◽  
Center Problem ◽  
Local Center ◽  
Third Order ◽  
Quadratic Systems ◽  
Necessary And Sufficient ◽  
Open Question

We obtain necessary and sufficient conditions for the existence of a center on a local center manifold for three 4-parameter families of quadratic systems on ℝ3. We also give a positive answer to an open question posed in [Dias & Mello, 2010] related to similar systems.

Center Problem for Quasi-Homogeneous Polynomial Systems with a Given Weight Degree

2018 ◽  
Vol 28 (14) ◽  
pp. 1850174 ◽  
Author(s):  
Yanqin Xiong ◽  
Jianqiang Hu ◽  
Shimin Li ◽  
Jingzheng Li
Keyword(s):  
Homogeneous Polynomial ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Polynomial Systems ◽  
Necessary And Sufficient Conditions ◽  
Center Problem ◽  
Necessary And Sufficient

This paper considers the center problem for quasi-homogeneous polynomial systems with a given weight degree. We provide the necessary conditions such that these systems have a center at the origin. Especially, we present the necessary and sufficient conditions on the existence of a center for some class of such systems.

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.

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.

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