一个周期边界条件下的Sturm-Liouville问题

An Sturm-Liouville problem with periodic boundary condition

研究了与常型Sturm-Liouville问题有密切联系的带有周期边界条件的Sturm-Liouville问题:Ly≡[-d2dx2+q(x)]y=λy,x∈[0,π],q(x)∈C2[0,π]y(0)=-y(π),y′(0)=-y′(π)得到了整函数ω(λ),并且证明了其零点集合与特征值集合重合,其零点重数与特征值的秩一致.

In the paper, an entire function ω（λ） are obtained for the following Sturm- Liouville problem with periodic boundary condition：（Ly=[-d^2/dx^2＋q（x）]y=λy,x∈[0,π],q（x）∈C^2[0,π] y（0）=-y（π） y′（0）=-y′（π））,The paper proves that the zero set of ω（λ） concedents the set of eigenvalue, the rank of the eigenvalue equals the order of the zero.