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Improper Singular Points of Corank 1 of Systems of Differential Equations Not Solved for the Derivatives

Improper Singular Points of Corank 1 of Systems of Differential Equations Not Solved for the... Differential Equations, Vol. 38, No. 8, 2002, pp. 1122–1131. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 8, 2002, pp. 1053–1062. Original Russian Text Copyright c 2002 by Remizov. ORDINARY DIFFERENTIAL EQUATIONS Improper Singular Points of Corank 1 of Systems of Di erential Equations Not Solved for the Derivatives A. O. Remizov Moscow State University, Moscow, Russia Received October 2, 2001 INTRODUCTION Consider a system of di erential equations not solved for the derivatives: F (t;x;p)= 0; p = dx=dt; (1) 1 n 1 n 1 n where x =(x ;:::;x ), p =(p ;:::;p ), and F =(F ;:::;F )are n-dimensional vectors. s+1 We assume that the function F (t;x;p)is jointly C -smooth, s  1, with respect to the ar- guments. A point T =(t ;x ;p )is saidto be admissible for Eq. (1) if F (t ;x ;p )= 0.In the 0 0 0 0 0 0 0 (2n + 1)-dimensional space (t;x;p), Eq. (1) determines the set F of admissible points. In general position, the set F is a smooth manifold of dimension n + 1. An admissible point T =(t;x;p)is said to be nonsingular if det(@F =@p) 6= 0 at that point. Otherwise, the point http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Improper Singular Points of Corank 1 of Systems of Differential Equations Not Solved for the Derivatives

Remizov, A.
Differential Equations , Volume 38 (8) – Oct 10, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2002 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1021616104228
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 38, No. 8, 2002, pp. 1122–1131. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 8, 2002, pp. 1053–1062. Original Russian Text Copyright c 2002 by Remizov. ORDINARY DIFFERENTIAL EQUATIONS Improper Singular Points of Corank 1 of Systems of Di erential Equations Not Solved for the Derivatives A. O. Remizov Moscow State University, Moscow, Russia Received October 2, 2001 INTRODUCTION Consider a system of di erential equations not solved for the derivatives: F (t;x;p)= 0; p = dx=dt; (1) 1 n 1 n 1 n where x =(x ;:::;x ), p =(p ;:::;p ), and F =(F ;:::;F )are n-dimensional vectors. s+1 We assume that the function F (t;x;p)is jointly C -smooth, s  1, with respect to the ar- guments. A point T =(t ;x ;p )is saidto be admissible for Eq. (1) if F (t ;x ;p )= 0.In the 0 0 0 0 0 0 0 (2n + 1)-dimensional space (t;x;p), Eq. (1) determines the set F of admissible points. In general position, the set F is a smooth manifold of dimension n + 1. An admissible point T =(t;x;p)is said to be nonsingular if det(@F =@p) 6= 0 at that point. Otherwise, the point

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Differential Equations – Springer Journals

Published: Oct 10, 2004

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