Difference boundary value problem hierarchies and the forward Crum transformation

Advances in Difference Equations

Anne D Love¹  Sonja Currie¹ 

[1] School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

关键词: difference equations;    hierarchies;    boundary value problems;    transformations;    Nevanlinna;    eigenvalues;   

DOI  :  10.1186/1687-1847-2013-311

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper uses the forward transformation defined in Currie and Love (Adv. Differ. Equ. 2010:947058, 2010) to develop a hierarchy for difference boundary value problems with eigenparameter-dependent boundary conditions. In particular, we show how various sets of these boundary conditions transform under this forward transformation. The resulting hierarchy is then illustrated in a tabular form where the number of eigenvalues for each of the problems is also given. In addition, we point out certain analogies to the work done in Currie and Love (Bound. Value Probl. 2011:743135, 2011) where the reverse Crum-type transformation was used to establish a hierarchy of difference boundary value problems. MSC:39A05, 34K10, 65Q10, 65Q30.

【 授权许可】

CC BY