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Oriented Degree of Fredholm Maps: Finite-Dimensional Reduction Method

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Abstract

The complete oriented degree theory for proper nonlinear Fredholm zero-index maps and their compact perturbations is constructed by means of a finite-dimensional reduction method. Applications to solvability and bifurcations of boundary-value problems for nonlinear elliptic equations are provided.

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  1. Voronezh State University, Voronezh, Russia

    V. G. Zvyagin & N. M. Ratiner

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  1. V. G. Zvyagin
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Correspondence to V. G. Zvyagin.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 44, Functional Analysis, 2012.

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Zvyagin, V.G., Ratiner, N.M. Oriented Degree of Fredholm Maps: Finite-Dimensional Reduction Method. J Math Sci 204, 543–714 (2015). https://doi.org/10.1007/s10958-015-2211-1

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