Comparison theorems for oscillation of second-order half-linear differential equations |
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Authors: | Jitsuro Sugie Naoto Yamaoka |
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Affiliation: | (1) Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan;(2) Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan |
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Abstract: | 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. |
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Keywords: | oscillation comparison theorems half-linear differential equations perturbation differential inequalities |
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