On complete solutions and complete singular solutions of second order ordinary differential equations

Masatomo Takahashi. "On complete solutions and complete singular solutions of second order ordinary differential equations." Colloquium Mathematicae 109.2 (2007): 271-285. <http://eudml.org/doc/283422>.

@article{MasatomoTakahashi2007,
abstract = {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.},
author = {Masatomo Takahashi},
journal = {Colloquium Mathematicae},
keywords = {implict differential equation; complete solution; singular solution; Clairaut equation},
language = {eng},
number = {2},
pages = {271-285},
title = {On complete solutions and complete singular solutions of second order ordinary differential equations},
url = {http://eudml.org/doc/283422},
volume = {109},
year = {2007},
}

TY - JOUR
AU - Masatomo Takahashi
TI - On complete solutions and complete singular solutions of second order ordinary differential equations
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 2
SP - 271
EP - 285
AB - 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.
LA - eng
KW - implict differential equation; complete solution; singular solution; Clairaut equation
UR - http://eudml.org/doc/283422
ER -