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Limit theorems for the solutions of multipoint boundary-value problems with parameter in Sobolev spaces. (English. Ukrainian original) Zbl 1461.34041

Ukr. Math. J. 72, No. 8, 1175-1184 (2021); translation from Ukr. Mat. Zh. 72, No. 8, 1015-1023 (2020).
The paper studies a general class of multipoint boundary value problems depending on a parameter \(\varepsilon>0\) and involving a system of linear ordinary differential equations of arbitrary order. The author proposes an asymptotic analysis of the solutions belonging to the complex Sobolev space \(W_{p}^{n+r}\) (with \(n\geq0\), \(r\geq1\), \(1\leq p\leq\infty\)) as \(\varepsilon\to 0^{+}\).

MSC:

34B08 Parameter dependent boundary value problems for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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