Geodesic
On complete solutions and complete singular solutions of second order ordinary differential equations
Masatomo Takahashi1
1 Department of Mathematics Hokkaido University Sapporo 060-0810, Japan
Colloquium Mathematicum, Tome 109 (2007) no. 2, pp. 271-285

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular solution of implicit second order ordinary differential equations.
DOI : 10.4064/cm109-2-9
Keywords: complete solution implicit second order ordinary differential equation defined immersive two parameter family geometric solutions equation hypersurface completely integrable equation either clairaut type first order type moreover define complete singular solution immersive one parameter family singular solutions contact singular set conditions existence complete solution complete singular solution implicit second order ordinary differential equations

Masatomo Takahashi 1

1 Department of Mathematics Hokkaido University Sapporo 060-0810, Japan 
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Masatomo Takahashi. On complete solutions and complete singular
 solutions of second order ordinary differential
 equations. Colloquium Mathematicum, Tome 109 (2007) no. 2, pp. 271-285. doi: 10.4064/cm109-2-9

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