Hnyp Y. Continuity in a parameter of solutions to one-dimensional boundary-value problems on Sobolev-Slobodetskii spaces

The thesis is devoted to the investigation of conditions for continuity in a parameter of solutions to the most general linear boundary-value problems for systems of ordinary differential equations of an arbitrary order with respect to the Sobolev space and for systems of first-order linear differential equations with respect to the Slobodetskii space. We prove that these problems are Fredholm with zero index and obtain a necessary and sufficient condition for their unique solvability. For the boundary-value problems depending on a parameter we establish a constructive criterion under which their solutions depend continuously on the parameter in the normed spaces respectively. We get a two-sided estimate for the degree of convergence of the solutions.