一类两个边界带谱参数的正则Sturm-Liouville算子的基本解的渐近分析

Asymptotic Analysis of a Class of Regular Sturm-Liouville Operators with Spectral-parameters in Two Boundary Conditions

研究了一类具有转换条件且两个边界条件中带谱参数的正则Sturm-Liouville问题.应用常数变易法导出Sturm-Liouville初值问题的一对线性无关的基本解的表达式,然后将该问题的基本解的渐近分析,转化为考虑定义在适当的Hilbert空间H中的一个线性自伴算子A的基本解的渐近分析,并推导出该正则的Sturm-Liouville算子A的基本解的渐近式和整函数的渐近式.

To investigate a class of regular Sturm-Liouville problems with transmission conditions and spectral-parameter in two boundary conditions,we applied the constants method to derive the expressions of a pair of linear independent fundamental solutions of Sturm-Liouville initial-value problems.Then a self-adjoint linear operator A ws defined in a suitable Hilbert space H such that the analysis of such problem were transformed into those of operator A.The asymptotic formulas of fundamental solutions of the regular Sturm-Liouville operator and integral function were also given.