Soldatov V. Continuity in a parameter of solutions to one-dimensional boundary-value problems in Holder spaces

In the thesis we investigate new classes of linear boundary-value problems for systems of ordinary differential equations, that are the broadest classes for systems of differential equations with solutions in Holder spaces or spaces of m times continuously differentiable functions. We prove the problems are Fredholm with zero index and establish a criterion for their unique solvability. For boundary-valued problems depending on a parameter we establish a constructive criterion under which their solutions are continuous in the parameter. We prove that the error and discrepancy of the solutions are of the same order. New wide classes of multipoint linear boundary-value problems depending on the parameter are introduced and investigated.