Acta Mathematica Hungarica

, Volume 111, Issue 1, pp 165–179

Comparison theorems for oscillation of second-order half-linear differential equations

  • Jitsuro Sugie
  • Naoto Yamaoka

DOI: 10.1007/s10474-006-0029-5

Cite this article as:
Sugie, J. & Yamaoka, N. Acta Math Hung (2006) 111: 165. doi:10.1007/s10474-006-0029-5


We establish new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equations. These improve the work of Elbert and Schneider [6] in which connections are found between half-linear differential equations and linear differential equations. Our comparison theorems are not of Sturm type or Hille--Wintner type which are very famous. We can apply the main results in combination with Sturm's or Hille--Wintner's comparison theorem to a half-linear differential equation of the general form (|x'|α-1x')' + a(t) |x|α-1x = 0.

oscillation comparison theorems half-linear differential equations perturbation differential inequalities 

Copyright information

© Springer-Verlag/Akadémiai Kiadó 2006

Authors and Affiliations

  • Jitsuro Sugie
    • 1
  • Naoto Yamaoka
    • 2
  1. 1.Department of Mathematics and Computer Science, Shimane University
  2. 2.Department of Mathematics and Computer Science, Shimane University

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