Masliuk H. One-dimensional boundary-value problems with parameter in function spaces of fractional smoothness

In the thesis we investigate new classes of linear boundary-value problems for systems of higher-order ordinary differential equations , that are the broadest classes for systems of differential equations with solutions in Holder spaces or Slobodetskii spaces. We prove the problems are Fredholm with zero index on a pair of function spaces 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 with respect to the parameter in the Holder spaces and constructive sufficient conditions of continuity in the Slobodetskii spaces. We prove that the error and discrepancy of the solutions are of the same order in the Holder spaces. New wide classes of multipoint linear boundary-value problems depending on the parameter are introduced. For such problems we establish sufficient conditions for their solutions to be continuous in the parameter in the Holder spaces. It is proved that the solution of an arbitrary boundary-value problem in the spaces of n+1 times continuously differentiable functions, can be approximated in this space with solutions of multipoint boundary-value problems.