边界条件含有特征参数的二阶离散Sturm-Liouville问题的谱

Spectra of a second order discrete Sturm-Liouville problem with a eigenparameter-dependent boundary condition

考虑边界条件含有特征参数的离散Sturm-Liouville问题-(p(t)Δy(t))+q(t)y(t)=λr(t)y(t),t∈[1,T]Z,b 0y(0)=d 0Δy(0),d 1λy(T+1)=y(T+1),其中[1,T]Z={1,2,…,T},r(t)>0,t∈[1,T]Z,得到了该问题特征值的重数、交错性以及特征函数的振荡性质.

Consider the spectra of a second order discrete Sturm-Liouville problem with eigenparameter dependent boundary condition-(p(t)Δy(t))+q(t)y(t)=λr(t)y(t),t∈[1,T]Z,b 0y(0)=d 0Δy(0),d 1λy(T+1)=y(T+1),where[1,T]Z={1,2,…,T},r(t)>0 for t∈[1,T]Z.The multiplicity and the interlacing properties of eigenvalues,and the oscillation properties of eigenfunctions are obtained.