Mathematics

1999, No. 4

S.V. Bogatyrev

The simple ecological model, which describes interaction of three populations a predator — two prey, is designed and investigated. We assume, that one prey is adapted to protection against a predator much worse another. The model is described by the singularly-perturbed system of the differential equations. We shall show, that in a usual situation the badly adapted prey is doomed on extinction. If to enter the mechanism of switching of a predator on spare kind of a prey, the badly adapted prey will survive.

I.H. Zainullin

EXISTENCE OF A LIPCHITZEAN SELECTION

It is obtained the suffcient conditions yieliding existence of a lipchitzean selection for compact valued maps. These results can be used in the stability theorems of solutions to differential inclusions.

O.F. Menshih

PERIODIC OSCILLATIONS OF THE SIMPLEST RELATIVISTIC MEMBRANE

An exact spherically symmetrical solution of the Born-Infeld equation in case of n-space variables has been obtained. This solution describes periodic oscillations of the relativistic membrane. If n=2 (cylindrical symmetry) this solutionmay be interpreted as pulsating oscillations of sphere. A formula determining a period of membrane oscillations for all values of n.

A.N. Stepanov

INTEGRAL PRESENTATION OF POTENTIAL THE PARAMETRIC MODEL OF POINT DIRECTIONAL SOURCE

Inheres a presentation of potential the parametric model of point directional source in uniform unlimited space in the manner of contour integral. Such presentation it is required for deciding the tasks in accordance with the determination of field considering source in limited areas. Proved that received presentation is exact.