scholarly journals On the Fiber Preserving Transformations for the Fifth-Order Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. Suksern ◽  
W. Pinyo
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Explicit Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linearization Problem ◽  
Necessary And Sufficient ◽  
Fifth Order

This paper is devoted to the study of the linearization problem of fifth-order ordinary differential equations by means of fiber preserving transformations. The necessary and sufficient conditions for linearization are obtained. The procedure for obtaining the linearizing transformations is provided in explicit form. Examples demonstrating the procedure of using the linearization theorems are presented.

scholarly journals Linearization of Fifth-Order Ordinary Differential Equations by Generalized Sundman Transformations

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Supaporn Suksern ◽  
Kwanpaka Naboonmee
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Linear Equation ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Order Ordinary Differential Equation ◽  
Linearization Problem ◽  
Necessary And Sufficient ◽  
Fifth Order

In this article, the linearization problem of fifth-order ordinary differential equation is presented by using the generalized Sundman transformation. The necessary and sufficient conditions which allow the nonlinear fifth-order ordinary differential equation to be transformed to the simplest linear equation are found. There is only one case in the part of sufficient conditions which is surprisingly less than the number of cases in the same part for order 2, 3, and 4. Moreover, the derivations of the explicit forms for the linearizing transformation are exhibited. Examples for the main results are included.

scholarly journals Stability of some differential equations of the fourth-order and fifth-order

2019 ◽  
pp. 18-27
Author(s):  
Boris S. Kalitine
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Classical Method ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Nonlinear Ordinary Differential Equations ◽  
Necessary And Sufficient ◽  
Positive Functions ◽  
Fifth Order

The article is devoted to the study of the problem of stability of nonlinear ordinary differential equations by the method of semi-definite Lyapunov’s functions. The types of fourth-order and fifth-order scalar nonlinear differential equations of general form are singled out, for which the sign-constant auxiliary functions are defined. Sufficient conditions for stability in the large are obtained for such equations. The results coincide with the necessary and sufficient conditions in the corresponding linear case. Studies emphasize the advantages in using the semi-positive functions in comparison with the classical method of applying Lyapunov’s definite positive functions.

scholarly journals Generalized Helicoidal Surfaces in Euclidean 5-space

2021 ◽  
Vol 29 (3) ◽  
pp. 269-283
Author(s):  
Ali Uçum ◽  
Makoto Sakaki
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Normal Curvature ◽  
Helicoidal Surfaces ◽  
Necessary And Sufficient

Abstract In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.

Oscillation of the Riemann–Weber Version of Euler Differential Equations with Delay

2000 ◽  
Vol 7 (3) ◽  
pp. 577-584
Author(s):  
Jitsuro Sugie ◽  
Mitsuru Iwasaki
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Oscillation Of Solutions

Abstract Our concern is to consider delay differential equations of Euler type. Necessary and sufficient conditions for the oscillation of solutions are given. The results extend some famous facts about Euler differential equations without delay.

Necessary and sufficient conditions for oscillation of nonlinear first-order forced differential equations with several delays of neutral type

Analysis ◽  
2019 ◽  
Vol 39 (3) ◽  
pp. 97-105 ◽  
Author(s):  
Sandra Pinelas ◽  
Shyam S. Santra
Keyword(s):  
Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
First Order ◽  
Several Delays ◽  
Necessary And Sufficient ◽  
T Tau ◽  
First Order Differential Equations

AbstractIn this work, necessary and sufficient conditions are obtained such that every solution of nonlinear neutral first-order differential equations with several delays of the form\bigl{(}x(t)+r(t)x(t-\tau)\bigr{)}^{\prime}+\sum_{i=1}^{m}\phi_{i}(t)H\bigl{(}% x(t-\sigma_{i})\bigr{)}=f(t)is oscillatory or tends to zero as {t\rightarrow\infty.} This problem is considered in various ranges of the neutral coefficient r. Finally, some illustrating examples are presented to show that feasibility and effectiveness of main results.

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