ONE-DIMENSIONAL PARAMETER-DEPENDENT BOUNDARY-VALUE PROBLEMS IN HOLDER SPACES

We study the most general class of linear boundary-value problems for systems of r-th order ordinary differential equations whose solutions range over the complex Holder space C-n+r,C-alpha, with 0 <= n epsilon Z and 0 < alpha <= 1. We prove a constructive criterion under which the solution to an arbitrary parameter-dependent problem from this class is continuous in C-n+r,C-alpha with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of this solution to the solution of the corresponding nonperturbed problem.