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

• Autorzy: Masatomo Takahashi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 34A26: Geometric methods in differential equations
• 34A09: Implicit equations, differential-algebraic equations
• 34C05: Location of integral curves, singular points, limit cycles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 2
• Strony: 271-285

Daty

wydano

2007

Twórcy

autor

Masatomo Takahashi

• Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Identyfikatory

DOI

10.4064/cm109-2-9