Oscillations in a delay-logistic equation

Gopalsamy, K.

doi:10.1090/qam/860898

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 \[ \frac {{dx\left ( t \right )}}{{dt}} = x\left ( t \right )\left \{ {a - \sum \limits _{j = 1}^n {{b_j}x\left ( {t - {\tau _j}} \right )} } \right \}\] and \[ \frac {{dx\left ( t \right )}}{{dt}} = x\left ( t \right )\left \{ {a - b\int _{ - \infty }^t {k\left ( {t - s} \right )x\left ( s \right )ds} } \right \}\] to be oscillatory about their respective positive steady states. The results are complementary to those in [15].

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