一类二阶离散左定Sturm-Liouville问题的谱

本文考虑二阶离散左定Sturm-Liouville (S-L)问题■的谱,这里[1,T]_Z={1,2,…,T},λ是谱参数,r(t)在[1,T]_Z上变号.本文得到了该问题特征值的存在性,交错性以及对应特征函数的振荡性.

Spectra of second order discrete left-definite Sturm-Liouville problems with eigenparameter dependent boundary conditions

Consider the spectra of the discrete second-order left definite Sturm-Liouville problem$$-nabla(p(t)Delta y(t))+q(t)y(t)=lambda r(t)y(t), tin[1,T]_mathbb{Z},$$$$(alambda+b)y(0)=(clambda+d)p(0)Delta y(0), y(T+1)=0,$$where $[1,T]_mathbb{Z}={1,2,cdots,T}$, $lambda$ is a spectral parameter, $r(t)$ changes its sign on $[1,T]_mathbb{Z}$. We obtain the existence and interlacing properties of the eigenvalues, the oscillation results of the eigenvalues of the above problem.