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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
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Abstract

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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