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Oscillatory Solutions for Second-Order Difference Equations in Hilbert Spaces

Advances in Difference Equations volume 2007, Article number: 086925 (2007) Cite this article

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 and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Málaga, 29071, Spain

    Cristóbal González & Antonio Jiménez-Melado

Authors
  1. Cristóbal González
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  2. Antonio Jiménez-Melado
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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

Keywords

  • Differential Equation
  • Hilbert Space
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis