Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales

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 dynamic equation on an arbitrary time scale TT, so that the well known case of differential dynamic systems (T=R)(T=R) and the recently developed case of discrete dynamic systems (T=Z)(T=Z) are unified. To the best of our knowledge, this is the first time that boundary value problems of dynamic equations on time scales have been dealt with by using critical point theory.