机构地区: 广东培正学院
出 处: 《广州大学学报(自然科学版)》 2009年第5期6-9,共4页
摘 要: 研究了一类具有转换条件且在两个边界条件中带谱参数的Sturm-Liouville问题.将上述问题的特征值和特征函数的研究,转化为考虑定义在适当的Hilbert空间H中的一个线性算子A的特征值和特征函数问题,即:使得上述问题的特征值等同于算子A的特征值,其特征函数等同于算子A相应的特征函数的第一个分量.同时,证明算子A的定义域D(A)在H中是稠密的和算子在H中是自伴的. This paper is to investigate a class of Sturm-Liouville operators with transmission conditions and spectral-parameter in two boundary conditions.A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues and eigenfunctions of such problem are transformed into those of operator A,i.e.,make the eigenvalues of the above problem equivalent to those of operator A,and its eigenfunctions equal to the first component of the corresponding eigenfunctions of operator A.At the s...