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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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