The equation y^′(t) = F(t, y(g(t)))

Muril Lynn Robertson

Vol. 43 (1972), No. 2, 483–491

DOI: 10.2140/pjm.1972.43.483

Abstract

A functional differential equation, in general, is a relationship in which the rate of change of the state of the system at time t depends on the state of the system at values of time, perhaps other than the present.

In this paper, sufficient conditions are given for g so that the initial value problem y′(t) = F(t,y(g(t))),y(p) = q, may be solved uniquely; where F is both continuous into the Banach space B, and is Lipschitzean in the second position.

Mathematical Subject Classification

Primary: 34G05

Secondary: 34A10

Milestones

Received: 4 August 1971

Published: 1 November 1972