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 |
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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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