Continuous dependence for two-point boundary value problems

Robert Gaines

Vol. 28 (1969), No. 2, 327–336

DOI: 10.2140/pjm.1969.28.327

Abstract

Suppose the boundary value problem

(1.1)

(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