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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

|x ' | α-1 x ' +a(t)|x| α-1 x=0


MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory