Sturmian comparison theory for half‐linear and nonlinear differential equations via Picone identity |
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| Authors: | Abdullah Özbekler |
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| Affiliation: | Department of Mathematics, Atilim University, Incek, Ankara, Turkey |
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| 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]( "urn:x-wiley:mma:media:mma4224:mma4224-math-0001") (1) and the second is the half‐linear differential equations ![urn:x-wiley:mma:media:mma4224:mma4224-math-0002]( "urn:x-wiley:mma:media:mma4224:mma4224-math-0002") (2) where Φα (s ) = |s |α ? 1s and α 1 > ? > α m > β > α m + 1 > ? > α n > 0. Under the assumption that the solution of 2 has two consecutive zeros, we obtain Sturm–Picone type and Leighton type comparison theorems for 1 by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for 1 . Examples are given to illustrate the relevance of the results. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | comparison Leighton mixed nonlinear nonselfadjoint Sturm– Picone Wirtinger |
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