Geodesic
Linear and logistic models with time dependent coefficients
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 91B62, 34G10, 34G20, 34K25, 00A71, 92D25
Keywords: growth models, linear model, logistic model, carrying capacity, product decomposition 
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     author = {Mir, Youness and Dubeau, Fran\c{c}ois},
     title = {Linear and logistic models with time dependent coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a11/}
}
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Mir, Youness; Dubeau, François. Linear and logistic models with time dependent coefficients. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a11/