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

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 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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