TERMINAL VALUE PROBLEMS FOR FIRST AND SECOND ORDER NONLINEAR EQUATIONS ON TIME SCALES.

In this paper we examine "terminal" value problems for dynamic equations on time scales -- that is, a dynamic equation whose solutions are asymptotic at infinity. We present a number of new theorems that guarantee the existence and uniqueness of solutions, as well as some comparison-type results. The methods we employ feature dynamic inequalities, weighted norms, and fixed-point theory. [ABSTRACT FROM AUTHOR]