论文摘要
本文研究了定义在有限区间（O,l）上的具有一般分离型边条件的左定Sturm-Liouville算子的特征函数的振荡问题。利用Prufer变换,给出了上述Sturm-Liouville算子特征值的符号指标的具体形式;得到了特征值的符号指标与Weyl函数以及Prufer角在该特征值处的罗朗展式（泰勒展式）的首项系数的符号之间的关系;这两个结果在形式上比P.Binding研究的具有一种特殊分离型边条件的左定Sturm-Liouville算子得到的结果要复杂,P.Binding得到的结果是本文的一种特例。最后,在上述两个结果的基础上给出了上述Sturm-Liouville算子的第n个正（负）特征值所对应的特征函数在[O,l]内的零点个数的计算公式,这是对P.Binding研究的具有一种特殊分离型边条件的左定Sturm-Liouville问题得到的计算特征函数零点个数的公式的推广。
论文目录
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标签：算子论文; 左定论文; 振荡问题论文; 函数论文; 特征值的符号指标论文;