2019
Том 71
№ 6

All Issues

Maslyuk H. O.

Articles: 2
Article (Ukrainian)

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

Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 404-411

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

Article (Ukrainian)

Continuity of the solutions of one-dimensional boundary-value problems in Hölder spaces with respect to the parameter

Maslyuk H. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 83-91

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 complex Hölder space $C^{n+r,\alpha} ([a, b])$, where $n \in Z_{+},\; 0 < \alpha \leq 1$ и $[a, b] \subset R$, and $[a, b] \subset R$. We establish sufficient conditions under which the solutions of these problems continuously depend on the parameter in the H¨older space $C^{n+r,\alpha} ([a, b])$.