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
| Christopher C. Tisdell |
School of Mathematics and Statistics
The University of New South Wales
Sydney NSW 2052, Australia
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