Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Necessary and sufficient conditions for the oscillations of a multiplicative delay logistic equation

Authors: S. R. Grace, I. Győri and B. S. Lalli
Journal: Quart. Appl. Math. 53 (1995), 69-79
MSC: Primary 34K15
DOI: https://doi.org/10.1090/qam/1315448
MathSciNet review: MR1315448
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Abstract: Necessary and sufficient conditions are presented for the oscillation of all positive solutions of the multiplicative delay logistic equation

$\displaystyle \frac{{dN\left( t \right)}}{{dt}} = r\left( t \right)N\left( t \r... ... \left( {\frac{{N\left( {g_j}\left( t \right) \right.}}{K}} \right) } } \right)$

about the positive equilibrium $ K$. The cases when $ r\left( t \right) = r$ and $ {g_j}\left( t \right) = t - {\tau _j}$ or $ {g_j}\left( t \right) = \left[ {t - {k_j}} \right]$, [*] denoting the greatest integer function, where $ r, {\tau _j}$, and $ {k_j}$ are positive constants, $ j = 1, 2,...,m$, are also included.

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DOI: https://doi.org/10.1090/qam/1315448
Article copyright: © Copyright 1995 American Mathematical Society

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