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

Summary 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.