scholarly journals Necessary and Sufficient Conditions for Finite Time Singularities in Ordinary Differential Equations

2000 ◽  
Vol 161 (2) ◽  
pp. 422-448 ◽  
Author(s):  
Alain Goriely ◽  
Craig Hyde
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Singularities ◽  
Necessary And Sufficient

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 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.

scholarly journals On necessary and sufficient conditions for output finite-time stability

Automatica ◽  
2021 ◽  
Vol 125 ◽  
pp. 109427
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient

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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