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Differential growth models for microbial populations

Jaroslav Milota (1982)

Aplikace matematiky

Two models of microbial growth are derived as a resuslt of a discussion of the models of Monod and Hinshelwood types. The approach takes account of the lyse of dead cells in inhibitory products as well as in those which stimulate the growth. The asymptotic behaviour of the models is proved and the models applied to a chemostat.

Disconjugacy and disfocality criteria for second order singular half-linear differential equations

Ondřej Došlý, Alexander Lomtatidze (1999)

Annales Polonici Mathematici

We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation u ' ' = p ( t ) | u | α | u ' | 1 - α s g n u + g ( t ) u ' , where α ∈ (0,1] and the functions p , g ∈ L l o c ( a , b ) are allowed to have singularities at the end points t = a, t = b of the interval under consideration.

Dispersions for linear differential equations of arbitrary order

František Neuman (1997)

Archivum Mathematicum

For linear differential equations of the second order in the Jacobi form y ' ' + p ( x ) y = 0 O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated.

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