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MATHEMATICS

On an extremal problem

V. A. Pchelintsev

Tomsk State University

Abstract: The paper consider the problem about a range $\Delta$ of some functional on a class of pairs functions univalent and meromorphic in a “circle–exterior of the circle” system. By means of the Goluzin variation method, it is possible to obtain a system of differential equations for boundary functions, and to find the equation of the boundary of range $\Delta$.

Keywords: class $\mathfrak M'$, functional, method of internal variations, variation formulas, necessary condition, boundary functions, differential equations.

UDC: 517.54

Received: 02.07.2012