Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Oscillations of the sunflower equation

Authors: M. R. S. Kulenović and G. Ladas
Journal: Quart. Appl. Math. 46 (1988), 23-28
MSC: Primary 34K15; Secondary 34C15
DOI: https://doi.org/10.1090/qam/934678
MathSciNet review: 934678
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Abstract: Consider the delay differential equation

$\displaystyle \ddot y\left( t \right) + \alpha \dot y\left( t \right) + \beta f\left( {y\left( {t - r} \right)} \right) = 0, \qquad \left( * \right)$

where $ \alpha , \beta $, and $ r$ are positive constants and $ f$ is a continuous function such that

$\displaystyle uf\left( u \right) > 0 \qquad for u \in \left[ { - A, B} \right], u \ne 0, and \mathop {\lim }\limits_{u \to 0} \frac{{f\left( u \right)}}{u} = 1,$

where $ A$ and $ B$ are positive numbers. When $ f\left( u \right) = \sin u, \left( * \right)$ is the so-called ``sunflower'' equation, which describes the motion of the tip of the sunflower plant.

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DOI: https://doi.org/10.1090/qam/934678
Article copyright: © Copyright 1988 American Mathematical Society

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