Asymptotic properties of solutions of a 2n(th)-order differential equationon a time scale

Authors
Anderson, D Peterson, A
Citation
D. Anderson et A. Peterson, Asymptotic properties of solutions of a 2n(th)-order differential equationon a time scale, MATH COMP M, 32(5-6), 2000, pp. 653-660
Citations number
8
Categorie Soggetti
Engineering Mathematics
Journal title
MATHEMATICAL AND COMPUTER MODELLING
ISSN journal
08957177 → ACNP
Volume
32
Issue
5-6
Year of publication
2000
Pages
653 - 660
Database
ISI
SICI code
0895-7177(200009)32:5-6<653:APOSOA>2.0.ZU;2-I
Abstract
In this paper, we are concerned with a 2n(th)-order linear self-adjoint dif ferential equation on a time scale. The results generalize known results fo r the corresponding ordinary differential equations and for difference equa tions. We define Type I and Type II solutions, prove the existence of these solutions, and verify asymptotic properties of these solutions. A quadrati c functional corresponding to the differential equation on a time scale is defined and is used to prove several of the results in this paper. (C) 2000 Elsevier Science Ltd. All rights reserved.