Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Oscillations in a delay-logistic equation


Author: K. Gopalsamy
Journal: Quart. Appl. Math. 44 (1986), 447-461
MSC: Primary 34K15; Secondary 92A15
DOI: https://doi.org/10.1090/qam/860898
MathSciNet review: 860898
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Abstract: Sufficient conditions are derived for all nonconstant nonnegative solutions of the equations of the form

$\displaystyle \frac{{dx\left( t \right)}}{{dt}} = x\left( t \right)\left\{ {a - \sum\limits_{j = 1}^n {{b_j}x\left( {t - {\tau _j}} \right)} } \right\}$

and

$\displaystyle \frac{{dx\left( t \right)}}{{dt}} = x\left( t \right)\left\{ {a - b\int_{ - \infty }^t {k\left( {t - s} \right)x\left( s \right)ds} } \right\}$

to be oscillatory about their respective positive steady states. The results are complementary to those in [15].

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DOI: https://doi.org/10.1090/qam/860898
Article copyright: © Copyright 1986 American Mathematical Society


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