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  • Research Article
  • Open Access

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

Journal of Inequalities and Applications20062006:42120

  • Received: 13 November 2005
  • Accepted: 30 January 2006
  • Published:


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.


  • Differential Equation
  • Continuous Function
  • Positive Constant
  • Asymptotic Behavior
  • Differentiable Function


Authors’ Affiliations

Department of Mathematics and Computer Science, Faculty of Science and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia and Montenegro
Department of Mathematics, Faculty of Science Education, Joetsu University of Education, Niigata 943-8512, Japan


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© J. Manojlovi´c and T. Tanigawa. 2006

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.