В работе получены оценки разности решений нелинейных и полулинейных дифференциальных уравнений в вещественном пространстве Банаха. In this paper we consider estimations of difference solutions of nonlinear differential equations in a Banach space.

In this paper we present the optimal control problem governed by a variational inclusion with the monotone operator and a quadratic costfunctional. We apply standart Galerkin method to the approximation of the problem. After giving some results on the existance of optimal control we shall prove the existance of weak condensation points of a set of solution of approximate problems. Each of these points is a solution of the initial optimization problem. Finally we shall give a simple example using the obtaned results.

In the paper there has been given an upper sharp estimation of the distance between the point f(z) and the boundary of the image f(B n) for biholomorphic mappings of the ball B n.

Рассматривается класс К n, nϵN, биголоморфных отображений f единичного шара В n на выпуклые области, f(0)=0, Df(0)=I. Известное в классическом случае n=1 точное неравенство (1+|z|) -2=|f'(z)|=(1-|z|) -2, z∈В 1, обобщалось разными авторами на многомерный случай с утверждением о точности соответствующих неравенств. Однако утверждение о точности таких неравенствах в ряде случаев ошибочно. Заметка нацелена на выявление таких случаев. In this paper there is considered the family К n, nϵN, of all f, f(0)=0, Df(0)=I, which map biholomorphically the unit ball B n onto convex domains in C n. Several authors generalized the well-known classical inequality (1+|z|) -2=|f'(z)|=(1-|z|) -2, z∈В 1, onto n-dimensional case; they have also declared that their inequalities are exact. In fact, in many cases the statemements were false. The intention of the paper is to indicate such cases

In this paper we give coefficient conditions for complex-valued harmonic functions that are ultivalent, sense-preserving and α-convex. We determine the extreme points, distortion and covering theorems for these mappings.

В статье изучается граничное поведение голоморфных функций, определенных в единичном шаре. In this paper we study the boundary behaviour of holomorphic functions defined in the unit ball

В статье показано, как, используя задачи экспериментальной математики, можно стимулировать самостоятельную работу и систематически побуждать учащихся к открытию собственных доказательств. The article is devoted to the course of Experimental Mathematics for students aged from 15 to 18. Course is founded on research problems different domains of mathematics.