Vol. 28, No. 2, 1969

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Continuous dependence for two-point boundary value problems

Robert Gaines

Vol. 28 (1969), No. 2, 327–336
Abstract

Suppose the boundary value problem

y′′ = f(t,y,y′)
(1.1)

y(a) = α, y(b) = β,
(1.2)

where f(t,y,y) is defined on D [a,b] × R2, has a unique solution y(t;α,β) which belongs to C2[a,b], for each (α,β) in some set S R2. This paper gives sufficient conditions for y(t;α,β), y(t;α,β), and y′′(t;α,β) to be continuous on [a,b] × S.

Mathematical Subject Classification
Primary: 34.36
Milestones
Received: 8 September 1967
Published: 1 February 1969
Authors
Robert Gaines