Results in Mathematics

, Volume 37, Issue 1–2, pp 56–83 | Cite as

Perturbations of the Half-Linear Euler Differential Equation

  • Á. Elbert
  • A. Schneider


Oscillation/nonoscillation properties of the perturbed half-linear Euler differential equation in the critical case are investigated. Strong connections are found between these half-linear differential equations and some linear differential equations, whose coefficient is the perturbation itself. In addition if the solutions of the corresponding linear differential equation satisfy two integral inequalities, then the asymptotic form of the solutions of the half-linear differential equation is established. Examples are given for the latter case.


Differential Equation Riccati Equation Linear Differential Equation Order Differential Equation Integral Inequality 
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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • Á. Elbert
    • 1
  • A. Schneider
    • 2
  1. 1.Budapest/Ungarn
  2. 2.Fachbereich MathematikUniversität DortmundDortmund

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