Oscillation Criterion for Half-Linear Differential Equations With Periodic Coefficients

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2012

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Academic Press inc Elsevier Science

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

In this paper, we present an oscillation criterion for second order half-linear differential equations with periodic coefficients. The method is based on the nonexistence of a proper solution of the related modified Riccati equation. Our result can be regarded as an oscillatory counterpart to the nonoscillation criterion by Sugie and Matsumura (2008). These two theorems provide a complete half-linear extension of the oscillation criterion of Kwong and Wong (2003) dealing with the Hill's equation. (C) 2012 Elsevier Inc. All rights reserved.

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Hilscher, Roman Simon/0000-0001-5844-4526; Ozbekler, Abdullah/0000-0001-5196-4078
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Hilscher, Roman Simon ORCID logo
Ozbekler, Abdullah ORCID logo

Keywords

Oscillation, Half-linear equation, Periodic coefficients, Modified Riccati equation, Hill's equation

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Q2

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Q2

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Volume

393

Issue

2

Start Page

360

End Page

366

URI

https://doi.org/10.1016/j.jmaa.2012.03.020
 https://hdl.handle.net/20.500.14411/326

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