标题： 带有贝塞尔型奇点的有限区间上的矩阵斯特姆-刘维尔方程 显示英文标题

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

摘要： 研究了在有限区间上具有贝塞尔型奇点的矩阵斯特姆-刘维尔方程。 构造了该方程的特殊基本解系：具有在奇点处指定行为的解析贝塞尔型解和具有大谱参数已知渐近性的比尔霍夫型解。 推导了连接这两个基本解系的斯托克斯乘子的渐近公式。 我们还设置了边界条件，并得到了边值问题的谱数据（特征值和权矩阵）的渐近公式。 我们的结果将在直接和反向谱问题的理论中有所帮助。 显示英文摘要

摘要： 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.