Matrix Sturm–Liouville equation with a Bessel-type singularity on a finite interval

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• 作者：Natalia Bondarenko
• 关键词：Matrix Sturm–Liouville equation ; Bessel ; type type singularity ; Spectral analysis ; Boundary value problem
• 刊名：Analysis and Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：7
• 期：1
• 页码：77-92
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1664-235X
• 卷排序：7

文摘

The matrix Sturm–Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.