Continuity in the parameter for the solutions of one-dimensional
boundary-value problems for differential equations of higher orders in Slobodetsky spaces
Authors
H. O. Maslyuk
V. A. Mikhailets
Abstract
We introduce the most general class of linear boundary-value problems for systems of ordinary differential equations of
order $r \geq 2$ whose solutions belong to the Slobodetsky space $^{Ws+r}_p\bigl(
(a, b),C_m\bigr),$
where $m \in N,\; s > 0$ and $p \in (1,\infty )$.
We also establish sufficient conditions under which the solutions of these problems are continuous functions of the parameter
in the Slobodetsky space $W^{s+r}_p\bigl(
(a, b),C_m\bigr)$.
