Geodesic
Fiber Completions, Contact Singularities and Single Valued Solutions for C ∞-Second Order Ode
Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 849-870

Voir la notice de l'article provenant de la source Cambridge University Press

An implicitly defined second order ODE is said to be singular if the second derivative cannot be smoothly written in terms of lower order variables. The standard existence and uniqueness theory cannot be applied to such ODE and the graphs of solutions may fail to be regular curves (i.e., the solutions may have isolated C 0-points or may fail to be single valued). In this paper we describe a local analysis for a large class of implicit second order ODE whose singular points satisfy a regularity condition. Within this class of ODE there is a secondary notion of (contact) singularity which is analogous to rest points for regular ODE. Theorems 5, 6, 7 and 8 produce invariants for these singularities which control the existence, uniqueness and the level of regularity in solutions.
DOI : 10.4153/CJM-1996-043-9
Mots-clés : 35A30, 35B32, 35F20 
Kossowski, Marek. Fiber Completions, Contact Singularities and Single Valued Solutions for C ∞-Second Order Ode. Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 849-870. doi: 10.4153/CJM-1996-043-9
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