Youness Mir, Francois Dubeau
Abstract:
We sutdy the effects of some properties of the carrying capacity on the
solution of the linear and logistic differential equations. We present
results concerning the behaviour and the asymptotic behaviour of their
solutions. Special attention is paid when the carrying capacity is an
increasing or a decreasing positive function. For more general carrying
capacity, we obtain bounds for the corresponding solution by constructing
appropriate subsolution and supersolution. We also present a decomposition
of the solution of the linear, and logistic, differential equation as a
product of the carrying capacity and the solution to the corresponding
differential equation with a constant carrying capacity.
Submitted May 22, 2015. Published January 11, 2016.
Math Subject Classifications: 91B62, 34G10, 34G20, 34K25, 00A71, 92D25
Key Words: Growth models; linear model; logistic model; carrying capacity;
product decomposition.
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Youness Mir Département de mathématiques Université de Sherbrooke, 2500 Boulevard de l'Université Sherbrooke (Qc), J1K 2R1, Canada email: youness.mir@usherbrooke.ca |
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François Dubeau Département de mathématiques Université de Sherbrooke 2500 Boulevard de l'Université Sherbrooke (Qc), J1K 2R1, Canada email: francois.dubeau@usherbrooke.ca |
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