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On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument

Abstract

The half-linear difference equations with the deviating argument , are considered. We study the role of the deviating argument , especially as regards the growth of the nonoscillatory solutions and the oscillation. Moreover, the problem of the existence of the intermediate solutions is completely resolved for the classical half-linear equation ( = 1). Some analogies or discrepancies on the growth of the nonoscillatory solutions for the delayed and advanced equations are presented; and the coexistence with different types of nonoscillatory solutions is studied.

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Correspondence to M. Cecchi.

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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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Cecchi, M., Došlá, Z. & Marini, M. On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument. Adv Differ Equ 2008, 505324 (2008). https://doi.org/10.1155/2008/505324

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation