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

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
\[ \left(| x'| ^{\alpha-1} x\right)'+a(t)| x| ^{\alpha-1} x=0 \]


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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