This article is cited in 8 papers

On relative compactness of a set of abstract functions in a scale of Banach spaces

A. G. Podgaev


Abstract: Theorems on compactness of sets in a scale of Banach spaces are established. The results can be used for proving solvability for abstract nonstationary nonlinear equations with operators having variable domains of definition as well as for nonlinear equations of mathematical physics in noncylindrical domains. Integrals for functions in a scale of spaces with respect to the scale parameter are introduced and their properties are given.

UDC: 517.95

Received: 28.08.1991

 English version: Siberian Mathematical Journal, 1993, 34:2, 320–329

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