Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 68, pp. 1-21.

Title: Terminal value problems for first and second
       order nonlinear equations on time scales
  
Authors: Roman Hilscher (Masaryk Univ.,  Janackovo, Brno, Czech Republic)
         Christopher C. Tisdell (Univ. of New South Wales, Sydney, Australia)

Abstract: 
  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.
 
Submitted February 11, 2008. Published May 01, 2008.
Math Subject Classifications: 34C99, 39A10.
Key Words: Time scale; terminal value problem; nonlinear equation;
           Banach fixed point theorem; bounded solution; weighted norm.