Eigenvalues of discrete Sturm-Liouville problems with eigenparameter dependent boundary conditions

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• 作者：Chenghua Gao^a ; ^b ; ^{gaokuguo@163.com" class="auth_mail" title="E-mail the corresponding author} ; Ruyun Ma^b
• 关键词：39A06 ; 39A12 ; 39A21 ; 39A70
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：503
• 期：Complete
• 页码：100-119
• 全文大小：451 K

文摘

We consider the discrete right definite Sturm–Liouville problems where [1,T]_Z={1,2,⋯,T}${[1,T]}_{\mathbb{Z}}=\{1,2,\cdots ,T\}$, m(t)>0$m(t)>0$ for t∈[1,T]_Z$t\in {[1,T]}_{\mathbb{Z}}$, (−1)ⁱδ_i≤0${(-1)}^i{\delta }_i\le 0$, where δ_i=a_id_i−b_ic_i${\delta }_i=a_i{d}_i-b_i{c}_i$ for i=0,1$i=0,1$. We obtain the existence of the eigenvalues, the sign-changing times of the eigenfunctions and the interlacing results of the eigenvalues of the above problem, the Dirichlet problem and the Neumann problem.