Open Access

Oscillatory Solutions for Second-Order Difference Equations in Hilbert Spaces

Advances in Difference Equations20072007:086925

DOI: 10.1155/2007/86925

Received: 16 March 2007

Accepted: 27 July 2007

Published: 10 September 2007

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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Authors’ Affiliations

(1)
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga

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Copyright

© C. González and A. Jiménez-Melado. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.