2019
Том 71
№ 6

Kodlyuk T. I.

Articles: 2
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.

Article (Russian)

Limit theorems for one-dimensional boundary-value problems

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 70-81

We study the limit with respect to a parameter in the uniform norm for solutions of general boundary-value problems for systems of linear ordinary differential equations of the first order. A generalization of the Kiguradze theorem (1987) to these problems is obtained. The conditions on the asymptotic behavior of the coefficients of the systems are weakened as much as possible. Sufficient conditions for the Green matrices to converge uniformly to the Green matrix of the limit boundary-value problem are found as well.