Limit theorems for general one-dimensional boundary-value problems

We investigate parameter-dependent general inhomogeneous boundary-value problems for systems of linear differential equations, of order n ∈ N, given on a finite interval. We find sufficient conditions under which the solutions to the problems together with their derivatives up to order n − 1 are continuous in the uniform norm with respect to the parameter. We also present sufficient conditions under which the Green matrices corresponding to these problems converge uniformly in the parameter. © 2014, Springer Science+Business Media New York.