2019
Том 71
№ 10

# Gnyp E. V.

Articles: 2
Article (Ukrainian)

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

Ukr. Mat. Zh. - 2016. - 68, № 6. - pp. 746-756

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.

Article (Russian)

### Fredholm Boundary-Value Problems with Parameter in Sobolev Spaces

Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 584-591

For systems of linear differential equations of order $r ∈ ℕ$, we study the most general class of inhomogeneous boundary-value problems whose solutions belong to the Sobolev space $W_p^{n + r} ([a, b],ℂ^m)$, where $m, n + 1 ∈ ℕ$ and $p ∈ [1,∞)$. We show that these problems are Fredholm problems and establish the conditions under which these problems have unique solutions continuous with respect to the parameter in the norm of this Sobolev space.