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Sufficient conditions are given
for the continuous dependence of solutions to the two-point boundary value
problem
 | (1) |
 | (2) |
on the boundary data and the parameter μ.
Previous results given by Gaines and Klaasen for continuous dependence on the
boundary data have assumed continuity on f and uniqueness to two-point BVP’S.
Klaasen has also shown assuming uniqueness to two-point BVP’S and the existence
of a C2-solution to (1) −(2) that there exist solutions x(t;α′,β′) to (1) with the
boundary conditions
for all (α′,β′) sufficiently close to (α,β). Furthermore, x(t;α′,β′) is a uniformly
continuous function of (α′,β′) at (α,β) on [a,b]. This same result is shown to be valid
under weaker uniqueness conditions. Sufficient conditions are also given for
existence and continuous dependence on the parameter, μ, of solutions to
(1)–(2).
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