Lyapunov type inequalities for second-order differential equations with mixed nonlinearities

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2016

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Walter de Gruyter GmbH

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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 some new Lyapunov and Hartman type inequalities for second-order equations with mixed nonlinearities: x''(t) + p(t)|x(t)|β?1x(t) + q(t)|x(t)|y?1x(t) = 0, where p(t), q(t) are real-valued functions and 0 < γ < 1 < β < 2. No sign restrictions are imposed on the potential functions p(t) and q(t). The inequalities obtained generalize the existing results for the special cases of this equation in the literature. © 2016 by De Gruyter.

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Keywords

Lyapunov type inequality, mixed nonlinear, sub-linear, super-linear

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1

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Source

Analysis (Germany)

Volume

36

Issue

4

Start Page

245

End Page

252

URI

https://doi.org/10.1515/anly-2015-0002
 https://hdl.handle.net/20.500.14411/3811

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