The Limit Point, Limit Circle Classification And Criteria For Second-order Equations On Time-scales

This paper is concerned with limit point case and limit circle case classification and criteria for singular second-order equations on time-scales. We construct a sequence of circles, these circles are nested and converge to a limiting set. By the different cases of the limiting set, we give limit point, limit circle classification and some criteria for second-order equations on time scales.The paper is mainly divided into five chapters.The first section is the introduction of the whole paper. We talk about the background of this paper, and make plans for the research of the problem.The second section introduces some concepts about time- scales and provides some theorems about derivative and integral on time-scales.The third section mainly give a dichotomy of the limit-point and limit-circle cases for a class of second-order singular differential equationson time-scales.The fourth section we present limit-point and limit-circle criteria for second-order equations on time-scales.At last, we summarize the whole paper.