Electron. J. Differential Equations,
Vol. 2017 (2017), No. 81, pp. 1-13.
Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces
Yevheniia Hnyp, Vladimir Mikhailets, Aleksandr Murach
Abstract:
We consider the most general class of linear boundary-value problems for
higher-order ordinary differential systems whose solutions and right-hand
sides belong to the corresponding Sobolev spaces. For parameter-dependent
problems from this class, we obtain a constructive criterion under which
their solutions are continuous in the Sobolev space with respect to the
parameter. We also obtain a two-sided estimate for the degree of convergence
of these solutions to the solution of the nonperturbed problem.
These results are applied to a new broad class of parameter-dependent
multipoint boundary-value problems.
Submitted January 16, 2017. Published March 24, 2017.
Math Subject Classifications: 34B08.
Key Words: Differential system; boundary-value problem; Sobolev space;
continuity in parameter.
Show me the PDF file (259 KB),
TEX file for this article.
 |
Yevheniia Hnyp
Institute of Mathematics
National Academy of Sciences of Ukraine
Tereshchenkivska Str. 3, 01004 Kyiv, Ukraine
email: evgeniyagnyp27@gmail.com
|
|---|
 |
Vladimir Mikhailets
Institute of Mathematics
National Academy of Sciences of Ukraine
Tereshchenkivska Str. 3, 01004 Kyiv, Ukraine
email: mikhailets@imath.kiev.ua
|
|---|
 |
Aleksandr Murach
Institute of Mathematics
National Academy of Sciences of Ukraine
Tereshchenkivska Str. 3, 01004 Kyiv, Ukraine
email: murach@imath.kiev.ua
|
|---|
Return to the EJDE web page