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

  • Ravi P. Agarwal and Abdullah Özbekler EMAIL logo
From the journal Analysis

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)|γ-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.

MSC 2010: 34C10

Funding statement: This work was partially supported by TUBITAK (Scientific and Technological Research Council of Turkey).

Acknowledgements

The second author wishes to thank Texas A&M University-Kingsville where this work was carried out when he was on academic leave.

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Received: 2015-1-5
Revised: 2016-1-13
Accepted: 2016-1-19
Published Online: 2016-1-27
Published in Print: 2016-11-1

© 2016 by De Gruyter

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