Fredholm boundary-value problems with a parameter on the spaces C(n)[a, b]

Abstract

We introduce and study boundary-value problems generated by the system of m ordinary linear differential equations of the first order and boundary conditions of the form By = c, where B: C⁽ⁿ⁾([a, b], C^m) → C^m is a continuous linear operator, and m, n are positive integers. We prove that such boundary-value problems possess the Fredholm property. Sufficient conditions for their solutions together with their derivatives up to order n to depend continuously on the parameter in the uniform norm are found.