Abstract
In this paper, Sturmian comparison theory is developed for the pair of second‐order differential equations; first of which is the nonlinear differential equations of the form urn:x-wiley:mma:media:mma4224:mma4224-math-0001 and the second is the half‐linear differential equations urn:x-wiley:mma:media:mma4224:mma4224-math-0002 where Φα(s) = |s|α − 1s and α1 > ⋯ > αm > β > αm + 1 > ⋯ > αn > 0. Under the assumption that the solution of has two consecutive zeros, we obtain Sturm–Picone type and Leighton type comparison theorems for by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for . Examples are given to illustrate the relevance of the results. Copyright © 2016 John Wiley & Sons, Ltd.
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