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.
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Yevheniia Hnyp Institute of Mathematics National Academy of Sciences of Ukraine Tereshchenkivska Str. 3, 01004 Kyiv, Ukraine email: evgeniyagnyp27@gmail.com |
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Vladimir Mikhailets Institute of Mathematics National Academy of Sciences of Ukraine Tereshchenkivska Str. 3, 01004 Kyiv, Ukraine email: mikhailets@imath.kiev.ua |
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Aleksandr Murach Institute of Mathematics National Academy of Sciences of Ukraine Tereshchenkivska Str. 3, 01004 Kyiv, Ukraine email: murach@imath.kiev.ua |
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