Fredholm Boundary-Value Problems with Parameter in Sobolev Spaces

• Date: 2015
• Main Authors: Gnyp, E. V., Kodlyuk, T. I., Mikhailets, V. A., Гнып, Е. В., Кодлюк, Т. И., Михайлец, В. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2006
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...