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Positivity

, Volume 20, Issue 2, pp 299–305 | Cite as

Asymptotic positivity of solutions of second order differential equations

  • Jaywan ChungEmail author
Article

Abstract

A body in a damped oscillator eventually stops at the origin. Can we drag the body to the positive side by giving a positive driving force? Unfortunately, due to the oscillatory motion of the body, it is not true in general. In this paper, we give a sufficient condition on the driving force guaranteeing the asymptotic positivity of the position of the body, which means the negative part of the position vanishes in time. Also the result will be extended to a wider class of differential equations including the damped oscillator.

Keywords

Second order linear differential equation Bounds Oscillating solutions Asymptotic positivity Gronwall’s inequality 

Mathematics Subject Classification

34C11 34E99 

Notes

Acknowledgments

This work was partially done when the author was in Laboratoire J.-L. Lions at Université Pierre-et-Marie Curie; the author would like to thank the Fondation Sciences Mathématiques de Paris for financial support.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.National Institute for Mathematical SciencesDaejeonKorea

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