Nonlinear differential equations from biology.

*(English)*Zbl 0539.35006
Nonlinear analysis, function spaces and applications, Vol. 2, Proc. Spring Sch., Písek/Czech. 1982, Teubner-Texte Math. 49, 93-125 (1982).

[For the entire collection see Zbl 0488.00011.]

In this paper the author shows that a certain epidemiological model is described by an infinite system of ordinary differential equations. Using a certain procedure, the author reduces this problem to a mixed problem. In the case in which the member of individuals does not depend on time, the mixed problem is reduced to a more simple problem for which the solution is explicitly obtained. Moreover, for this case the behaviour of stationary solutions is studied.

The author has also studied some biological models which are described by Neumann problems for the diffusion equation and a model from population genetics. For the last model he has studied the behaviour of stationary points. Some other interesting models of differential equations are studied both from a theoretical and applicational point of view.

In this paper the author shows that a certain epidemiological model is described by an infinite system of ordinary differential equations. Using a certain procedure, the author reduces this problem to a mixed problem. In the case in which the member of individuals does not depend on time, the mixed problem is reduced to a more simple problem for which the solution is explicitly obtained. Moreover, for this case the behaviour of stationary solutions is studied.

The author has also studied some biological models which are described by Neumann problems for the diffusion equation and a model from population genetics. For the last model he has studied the behaviour of stationary points. Some other interesting models of differential equations are studied both from a theoretical and applicational point of view.

Reviewer: N.Luca

##### MSC:

35B40 | Asymptotic behavior of solutions to PDEs |

92D25 | Population dynamics (general) |

35F30 | Boundary value problems for nonlinear first-order PDEs |

35J60 | Nonlinear elliptic equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |