This article is cited in 29 papers

The degree of a quasi-ruled mapping and a nonlinear Hilbert problem

A. I. Shnirel'man


Abstract: In this paper we present the theory of the degree of a mapping for a class, containing nonlinear (pseudo) differential operators, of nonlinear mappings in Banach spaces. This theory is applied to prove the existence of solutions to nonlinear boundary value problems in the theory of analytic functions, under some purely topological hypotheses.
Bibliography: 11 titles.

UDC: 517.54

MSC: Primary 30A88, 55C25; Secondary 30A30, 45G05

Received: 13.12.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 18:3, 373–396

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