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A boundary value problem for second-order nonlinear difference equations on the integers

Published online by Cambridge University Press:  17 February 2009

F. Dal  and
G. Sh. Guseinov
F. Dal
Affiliation:
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey.
G. Sh. Guseinov
Affiliation:
Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey; e-mail: guseinov@atilim.edu.tr.
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Abstract

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In this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z. under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l2 and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 2 , October 2005 , pp. 237 - 248
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Agarwal, R. P., Bohner, M. and O'Regan, D., “Time scale systems on infinite intervals”, Nonlinear Anal. 47 (2001) 837–848.CrossRefGoogle Scholar
[2]Agarwal, R. P., Bohner, M. and O'Regan, D., “Time scale boundary value problems on infinite intervals”, J. Comput. Appl. Math. 141 (2002) 27–34.CrossRefGoogle Scholar
[3]Agarwal, R. P. and O'Regan, D., “Boundary value problems for general discrete systems on infinite intervals”, Comput. Math. Appl. 33 (1997) 85–99.CrossRefGoogle Scholar
[4]Agarwal, R. P. and O'Regan, D., “Discrete systems on infinite intervals”, Comput. Math. Appl. 35 (1998) 97–105.CrossRefGoogle Scholar
[5]Berezanskii, Yu. M., Expansion in eigenfunctions of selfadjoint operators (Naukova Dumka, Kiev, 1965). English translation: (Amer. Math. Soc., Providence, RI, 1968).Google Scholar
[6]Dal, F. and Guseinov, G. Sh., “Properties of discrete composition operators”, J. Differ. Equations Appl. 11 (2005) 21–27.CrossRefGoogle Scholar
[7]Guseinov, G. Sh., “A boundary value problem for second order nonlinear difference equations on the semi-infinite interval”, J. Differ. Equations Appl. 8 (2002) 1019–1032.CrossRefGoogle Scholar
[8]Guseinov, G. Sh. and Yaslan, I., “Boundary value problems for second order nonlinear differential equations on infinite intervals”, J. Math. Anal. Appl. 290 (2004) 620–638.CrossRefGoogle Scholar