Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-23T08:41:33.976Z Has data issue: false hasContentIssue false

Difference equations in abstract spaces

Published online by Cambridge University Press:  09 April 2009

Ravi P. Agarwal
Affiliation:
Department of Mathematics National University of SingaporeKent RidgeSingapore119260
Donal O'Regan
Affiliation:
Department of Mathematics University College GalwayGalway, Ireland
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.

Existence results are presented for second order discrete boundary value problems in abstract spaces. Our analysis uses only Sadovskii's fixed point theorem.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Agarwal, R. P., ‘On boundary value problems for second order discrete systems’, Appl. Anal. 20 (1985), 117.CrossRefGoogle Scholar
[2]Agarwal, R. P., Difference equations and inequalities (Marcel Dekker, New York, 1992).Google Scholar
[3] R. P. Agarwal and D. O'regan, ‘A fixed point approach for nonlinear discrete boundary value problems’, Comput. Math. Appl. to appear.Google Scholar
[4]Dugundji, J. and Granas, A., Fixed point theory, Monografie Mat. (PWN, Warsaw, 1982).Google Scholar
[5]Frigon, M. and O'Regan, D., ‘Nonlinear first order initial and periodic problems in Banach spaces’, Appl. Math. Lett. 10 (1997), 4146.CrossRefGoogle Scholar
[6]Frigon, M. and O'Regan, D., ‘Existence results for initial value problems in Banach spaces’, Differential Equations Dynamical Systems 2 (1994), 4148.Google Scholar
[7]Lakshmikantham, V. and Leela, S., Nonlinear differential equations in abstract spaces (Pergamon Press, New York, 1981).Google Scholar
[8]Lasota, A., ‘A discrete boundary value problem’, Ann. Polon. Math. 20 (1968), 183190.CrossRefGoogle Scholar
[9]Zhuang, W., Chen, Y. and Cheng, S. S., ‘Monotone methods for a discrete boundary problem’, Comput. Math. Appl. 32 (1996), 4149.CrossRefGoogle Scholar