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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2022, том 13, номер 3, страницы 82–91 (Mi emj448)

Эта публикация цитируется в 4 статьях

Asymptotics of solutions of boundary value problems for the equation $\varepsilon y''+xp(x)y'-q(x)y=f$

D. A. Tursunov, K. G. Kozhobekov, Bekmurza uulu Ybadylla

Osh State University, 331 Lenin St, Osh, Kyrgyzstan

Аннотация: Uniform asymptotic expansions of solutions of two-point boundary value problems of Dirichlet, Neumann and Robin for a linear inhomogeneous ordinary differential equation of the second order with a small parameter at the highest derivative are constructed. A feature of the considered two-point boundary value problems is that the corresponding unperturbed boundary value problems for an ordinary differential equation of the first order has a regularly singular point at the left end of the segment. Asymptotic solutions of boundary value problems are constructed by the modified Vishik-Lyusternik-Vasilyeva method of boundary functions. Asymptotic expansions of solutions of two-point boundary value problems are substantiated. We propose a simpler algorithm for constructing an asymptotic solution of bisingular boundary value problems with regular singular points, and our boundary functions constructed in a neighborhood of a regular singular point have the property of "boundary layer", that is, they disappear outside the boundary layer.

Ключевые слова и фразы: asymptotic solution, Dirichlet boundary value problem, Neumann boundary value problem, Robin boundary-value problem, bisingularly perturbed problem, small parameter, regularly singular point.

MSC: 34E05, 34E10, 34B15, 34E20

Поступила в редакцию: 03.05.2021

Язык публикации: английский

DOI: 10.32523/2077-9879-2022-13-3-82-91



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