The Darboux property and solutions of algebraic differential equations

Andrew Michael Bruckner, Melvin Rosenfeld and Lee Albert Rubel

Vol. 118 (1985), No. 2, 295–302

DOI: 10.2140/pjm.1985.118.295

Abstract

The most basic notion of a solution of a differential equation is that of a function that is differentiable enough to plug into it (without demanding continuity of the derivatives of highest order) and that, of course, makes the equation a true statement when you do plug it in. The lack of continuity of the derivatives has posed many obstacles in treating these solutions. In this paper we overcome several of these obstacles in the case of algebraic differential equations by using the Darboux property of derivatives.

Mathematical Subject Classification 2000

Secondary: 12H05

Milestones

Received: 16 April 1984

Published: 1 June 1985