Comparison theorems for oscillation of second order half-linear differential equations. (English) Zbl 1116.34030

Sugie, J.; Yamaoka, N.

Acta Math. Hung. 111, No. 1-2, 165-179 (2006).

There are established new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equation. Connections between half-linear differential equation and linear differential equations are found. The comparison theorems from this work are not of Sturm type or Hill-Wintner type, but the main results are applied in combination with Sturm or Hille-Wintner comparison theorems to the half-linear differential equation of the general form
\[ \left(| x'| ^{\alpha-1} x\right)'+a(t)| x| ^{\alpha-1} x=0 \]

Reviewer: Vasile Marinca (Timisoara)

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

perturbation; differential inequalities