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Oscillatory Solutions for Second-Order Difference Equations in Hilbert Spaces

Abstract

We consider the difference equation , , in the context of a Hilbert space. In this setting, we propose a concept of oscillation with respect to a direction and give sufficient conditions so that all its solutions be directionally oscillatory, as well as conditions which guarantee the existence of directionally positive monotone increasing solutions.

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Correspondence to Cristóbal González.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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González, C., Jiménez-Melado, A. Oscillatory Solutions for Second-Order Difference Equations in Hilbert Spaces. Adv Differ Equ 2007, 086925 (2007). https://doi.org/10.1155/2007/86925

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  • DOI: https://doi.org/10.1155/2007/86925

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