Electron. J. Diff. Equ., Vol. 2016 (2016), No. 18, pp. 1-17.

Linear and logistic models with time dependent coefficients

Youness Mir, Francois Dubeau

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
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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