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Mediterranean Journal of Mathematics

, Volume 13, Issue 5, pp 2383–2396 | Cite as

Oscillation Criteria for Certain Fourth-Order Nonlinear Delay Differential Equations

  • Said R. Grace
  • Shurong Sun
  • Elvan Akın
Article

Abstract

In this article, we establish some new criteria for the oscillation of fourth-order nonlinear delay differential equations of the form
$$(r_2(t)(r_1(t)(y''(t))^\alpha)')' + p(t)(y''(t))^\alpha + q(t)f(y(g(t))) = 0$$
provided that the second-order equation
$$(r_2(t)z'(t))') + \frac{p(t)}{r_1(t)}z(t) = 0$$
is nonoscillatory or oscillatory.

Keywords

Oscillation fourth order functional differential equation 

Mathematics Subject Classification

34C10 39A10 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Engineering Mathematics, Faculty of EngineeringCairo UniversityOrmanEgypt
  2. 2.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China
  3. 3.Department of Mathematics and StatisticsMissouri University of Science and TechnologyRollaUSA

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