Oscillatory Solutions for Second-Order Difference Equations in Hilbert Spaces
We consider the difference equation Open image in new window , Open image in new window , 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.
KeywordsDifferential Equation Hilbert Space Partial Differential Equation Ordinary Differential Equation Functional Analysis
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