2019
Том 71
№ 11

All Issues

Continuity in the parameter for the solutions of one-dimensional boundary-value problems for differential equations of higher orders in Slobodetsky spaces

Maslyuk H. O., Mikhailets V. A.


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 $W^{s+r}_p\bigl( (a, b),C_m\bigr)$.

Citation Example: Maslyuk H. O., Mikhailets V. A. Continuity in the parameter for the solutions of one-dimensional boundary-value problems for differential equations of higher orders in Slobodetsky spaces // Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 404-411.