Acta Mathematica Hungarica

, Volume 120, Issue 1–2, pp 147–163 | Cite as

Conditionally oscillatory half-linear differential equations

Article

Abstract

We consider a nonoscillatory half-linear second order differential equation
$$ (r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x) = \left| x \right|^{p - 2} x,p > 1, $$
(*)
and suppose that we know its solution h. Using this solution we construct a function d such that the equation
$$ (r(t)\Phi (x'))' + [c(t) + \lambda d(t)]\Phi (x) = 0 $$
(**)
is conditionally oscillatory. Then we study oscillations of the perturbed equation (**). The obtained (non)oscillation criteria extend existing results for perturbed half-linear Euler and Euler-Weber equations.

Key words and phrases

half-linear oscillation theory conditionally oscillatory equation oscillation and nonoscillation criteria Riccati type equation 

2000 Mathematics Subject Classification

34C10 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic
  2. 2.Faculty of EngineeringBahcesehir UniversityBesiktas, IstanbulTurkey

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