Classification and criteria of the limit cases for singular second-order linear equations on time scales
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
Boundary Value Problems 2012, 2012:103 doi:10.1186/1687-2770-2012-103Published: 19 September 2012
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.