Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-29T12:49:12.366Z Has data issue: false hasContentIssue false
  • English
  • Français

Growth theorems for homogeneous second-order difference equations

Published online by Cambridge University Press:  17 February 2009

Stevo Stević
Stevo Stević
Affiliation:
Matematički Fakultet, Studentski Trg 16, 11000 Beograd, Yugoslavia; e-mail: sstevo@matf.bg.ac.yu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we investigate the boundedness and asymptotic behaviour of the solutions of a class of homogeneous second-order difference equations with a single non-constant coefficient. These equations model, for example, the amplitude of oscillation of the weights on a discretely weighted vibrating string. We present several growth theorems. Two examples are also given.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 4 , April 2002 , pp. 559 - 566
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Atkinson, F. V., Discrete and Continuous Boundary Problems (Academic Press, 1964).Google Scholar
[2]Bellman, R., “The stability of solutions of linear differential equations”, Duke Math. J. 10 (1943) 643–647.CrossRefGoogle Scholar
[3]Bellman, R., Stability Theory of Differential Equations (McGraw-Hill, New York, 1953).Google Scholar
[4]De Blasi, F. S. and Schinas, J., “On the stability of difference equations in Banach spaces”, Analele stintficae ale Universitatii Al. Cuza, lasi Sectia la. Matematica 20 (1974) 65–80.Google Scholar
[5]Fort, T., Finite Differences and Difference Equations in the Real Domain (Oxford Univ. Press, London, 1948).Google Scholar
[6]Gronwall, T., “Note on the derivatives with respect to a parameter of the solutions of a system of differential equations”, Ann. Math. 20 (2) (1919) 292–296.CrossRefGoogle Scholar
[7]Kelly, W. G. and Petersen, A. C., Difference Equations: An Introduction with Applications (Academic Press, Boston, 1991).Google Scholar
[8]Kurpinar, E. and Guseinov, G. Sh., “The boundedness of solutions of the second-order difference equations”, Indian J. Math. 37 (2) (1995) 113–122.Google Scholar