Fredholm Boundary-Value Problems with Parameter in Sobolev Spaces

被引：0

作者：

E. V. Gnyp

T. I. Kodlyuk

V. A. Mikhailets

机构：

[1] Ukrainian National Academy of Sciences,Institute of Mathematics

[2] Ternopil’ National Pedagogic University,undefined

[3] “Kyiv Polytechnic Institute” Ukrainian National Technical University,undefined

来源：

Ukrainian Mathematical Journal | 2015年 / 67卷

关键词：

Banach Space; Cauchy Problem; Sobolev Space; Vector Function; Matrix Function;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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 Wpn + r ([a, b],ℂm), 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.

引用

页码：658 / 667

页数：9

共 12 条

[1] Kodlyuk TI(2013)Limit theorems for one-dimensional boundary-value problems Ukr. Math. J. 65 77-90
[2] Mikhailets VA(2003)On boundary-value problems for linear differential systems with singularities Differents. Uravn. 39 198-209
[3] Reva NV(2015)Limit theorems for general one-dimensional boundary-value problems J. Math. Sci. 204 333-342
[4] Kiguradze IT(2013)Solutions of one-dimensional boundary-value problems with a parameter in Sobolev spaces J. Math. Sci. 190 589-599
[5] Mikhailets VA(2010)Resolvent convergence of Sturm–Liouville operators with singular potentials Math. Notes 87 287-292
[6] Chekhanova GA(2010)Regularization of singular Sturm–Liouville equations Meth. Funct. Anal. Topol. 16 120-130
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