边界条件含有特征参数的2×2 Sturm-Liouville问题特征值的迹公式

Trace Formula of 2×2 Sturm-Liouville Eigenvalue Problem under Boundary Conditions with Eigenparameters

讨论了边界条件含有特征参数的2×2 Sturm-Liouville特征值问题.首先将特征值的存在性问题化为一个整函数零点的存在性问题.然后借助于一个积分恒等式,采用留数方法,得到了边界条件含有特征参数的2×2 Sturm-Liouville问题特征值的迹公式.

In this paper,2×2 Sturm-Liouville eigenvalue problem under boundary conditions with eigenparameters is discussed.The existence of eigenvalue problem into the zeroes of entire function.By restorting to the integral identity and using the residue method,the trace formula of 2×2 Sturm-Liouville eigenvalue problem under boundary conditions with eigenparameters is obtained.