Existence Of Weak Solutions Of Two-point Boundary Value Problems For Second-order And Four-order Dynamic Equations On Time Scales

We assume T is an arbitrary time scale, a is the forward jump operator.Firstly, we consider the existence of weak solutions of two point boundary value problem for a second order dynamic equation where/has asymptotically linear behaviour. We use the critical point theory to prove the existence of weak solutions for problem (3). This is a supplement for the research results of Liqun Jiang and Zhan Zhou in.Secondly, we extend the result of second order dynamic equation to two point boundary value problem for four order dynamic equationThis is an extension in time scale for the results of Huansong Zhou in.In this paper, by using critical point theory, we establish the existence of weak solutions of the two-point boundary value problem for a second-order and a four-order dynamic equation on an arbitrary time scale T.