On calculation of the relative index of a fixed point in the nondegenerate case

Guminskaya, A. V.; Zabreiko, P. P.

doi:https://doi.org/10.1155/AAA/2006/86173

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Topological and variational methods of nonlinear analysis and their applications

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Volume 2006 | Article ID 086173 | https://doi.org/10.1155/AAA/2006/86173

On calculation of the relative index of a fixed point in the nondegenerate case

A. V. Guminskaya¹and P. P. Zabreiko¹

Received26 Jun 2005

Accepted01 Jul 2005

Published11 Apr 2006

Abstract

The paper is devoted to the calculation of the index of a zero and the asymptotic index of a linear completely continuous nonnegative operator. Also the case of a nonlinear completely continuous operator A whose domain and image are situated in a closed convex set Q of a Banach space is considered. For this case, we formulate the rules for calculating the index of an arbitrary fixed point and the asymptotic index under the assumption that the corresponding linearizations exist and the operators of derivative do not have eigenvectors with eigenvalue 1 in some wedges.

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Copyright

Copyright © 2006 A. V. Guminskaya and P. P. Zabreiko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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