Asymptotic properties of solutions of a 2nth-order differential equation on a time scale

In this paper, we are concerned with a 2nth-order linear self-adjoint differential equation on a time scale. The results generalize known results for the corresponding ordinary differential equations and for difference equations. We define Type I and Type II solutions, prove the existence of these solutions, and verify asymptotic properties of these solutions. A quadratic functional corresponding to the differential equation on a time scale is defined and is used to prove several of the results in this paper.