Electron. J. Diff. Eqns., Vol. 2008(2008), No. 68, pp. 1-21.

Terminal value problems for first and second order nonlinear equations on time scales

Roman Hilscher, Christopher C. Tisdell

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 1, 2008.
Math Subject Classifications: 34C99, 39A10.
Key Words: Time scale; terminal value problem; nonlinear equation; Banach fixed point theorem; bounded solution; weighted norm.

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Roman Hilscher
Department of Mathematics and Statistics
Faculty of Science, Masaryk University
Janackovo nam. 2a, CZ-60200 Brno, Czech Republic
email: hilscher@math.muni.cz
Christopher C. Tisdell
School of Mathematics and Statistics
The University of New South Wales
Sydney NSW 2052, Australia
email: cct@unsw.edu.au

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