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Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations. (English) Zbl 1036.39018
The authors give a criterion for the existence of bounded nonoscillatory solutions for a higher order nonlinear neutral difference equation. Their results extend those of F. Yang and J. Liu [J. Syst. Sci. Math. Sci. 22, No. 1, 85–89 (2002; Zbl 0999.39009)], Y. Zhou [Appl. Math. Lett. 15, 785–791 (2002; Zbl 1029.39009)] and J. R. Graef and E. Thandapani [J. Math. Anal. Appl. 224, No. 2, 349–355 (1998; Zbl 0923.39006)]. The proofs use Krasnoselskii’s fixed point theorem.

MSC:
39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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