Open Access Research

Classification and criteria of the limit cases for singular second-order linear equations on time scales

Chao Zhang1* and Yuming Shi2

Author Affiliations

1 School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, P.R. China

2 Department of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China

For all author emails, please log on.

Boundary Value Problems 2012, 2012:103  doi:10.1186/1687-2770-2012-103

Published: 19 September 2012

Abstract

This paper is concerned with classification and criteria of the limit cases for singular second-order linear equations on time scales. By the different cases of the limiting set, the equations are divided into two cases: the limit-point and limit-circle cases just like the continuous and discrete cases. Several sufficient conditions for the limit-point cases are established. It is shown that the limit cases are invariant under a bounded perturbation. These results unify the existing ones of second-order singular differential and difference equations.

Keywords:
singular second-order linear equation; time scales; limit-point case; limit-circle case