Conitnuity of the solutions of one-dimensional boundary-value problems with respect to the parameter in slobodetsky spaces

Abstract

For the system of linear ordinary differential equations of the first order, we study the broadest class of inhomogeneous boundary-value problems whose solutions belong to the Slobodetsky space $W^{s+1}_p ((a, b),C^m)$ with $m \in N,\; s > 0$, and $p \in (1,\infty )$. We prove a theorem on the Fredholm property of these problems. We also establish conditions under which the problems are uniquely solvable in the Slobodetsky space and their solutions are continuous in this space with respect to the parameter.