具有奇异势的 Sturm-Liouville 算子带参数问题解的渐近特性研究

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-07-08 DOI:10.1134/s0012266124030017

I. S. Lomov

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引用次数: 0

摘要

摘要带奇异势的 Sturm-Liouville 算子定义在一个重线段上。在区间的内点规定了传递条件。算子势可能具有不可解奇点。对于带参数方程的考希问题的强解，在每个解的平滑区间上都得到了渐近公式和估计值。

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Study of the Asymptotic Properties of the Solution to a Problem with a Parameter for the Sturm–Liouville Operator with a Singular Potential

Abstract

The Sturm–Liouville operator with a singular potential is defined on an interval of the real line. Transmission conditions are specified at an interior point of the interval. The operator potential may have a nonintegrable singularity. For the strong solution of the Cauchy problem for an equation with a parameter, asymptotic formulas and estimates are obtained on each of the solution smoothness intervals.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.