The extendability and uniqueness of solutions of ordinary differential equations

Stephen Richard Bernfeld

Vol. 69 (1977), No. 2, 307–315

DOI: 10.2140/pjm.1977.69.307

Abstract

The extendability of solutions of ordinary differential equations is a fundamental and important property since the analysis of stability and boundedness of solutions requires extendability. This paper is concerned with the preservation of the extendability and uniqueness of solutions under perturbations. In particular conditions on the right hand side of ẋ = f(x) + h(t) are exhibited which guarantee the extendability of solutions whenever the solutions of the unperturbed equation ẋ = f(x) extend.

Mathematical Subject Classification

Primary: 34A15, 34A15

Milestones

Received: 4 November 1976

Published: 1 April 1977