- Turkish Journal of Mathematics
- Vol: 40 Issue: 2
- Quadraticeigenparameter-dependent quantum difference equations
Quadraticeigenparameter-dependent quantum difference equations
Authors : Yelda Aygar Küçükevcilioğlu
Pages : 445-452
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :The main aim of this paper is to construct quantum extension of the discrete Sturm--Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. We present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.Keywords : $q$-difference equation, Jost solution, spectral analysis, eigenvalue, spectral singularity