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Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations

Journal of Inequalities and Applications volume 2006, Article number: 42120 (2006) Cite this article

Abstract

We are concerned with the oscillatory and nonoscillatory behavior of solutions of even-order quasilinear functional differential equations of the type, where and are positive constants, and are positive continuous functions on, and is a continuously differentiable function such that,. We first give criteria for the existence of nonoscillatory solutions with specific asymptotic behavior, and then derive conditions (sufficient as well as necessary and sufficient) for all solutions to be oscillatory by comparing the above equation with the related differential equation without deviating argument.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia and Montenegro

    Jelena Manojlović

  2. Department of Mathematics, Faculty of Science Education, Joetsu University of Education, Niigata, 943-8512, Japan

    Tomoyuki Tanigawa

Authors
  1. Jelena Manojlović
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  2. Tomoyuki Tanigawa
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Correspondence to Tomoyuki Tanigawa.

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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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Manojlović, J., Tanigawa, T. Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations. J Inequal Appl 2006, 42120 (2006). https://doi.org/10.1155/JIA/2006/42120

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  • DOI: https://doi.org/10.1155/JIA/2006/42120

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