Abstract and Applied Analysis
Volume 2006 (2006), Article ID 86173, 11 pages
On calculation of the relative index of a fixed point in the nondegenerate case
Mechanics and Mathematics Faculty, Belarusian State University, Independence Avenue 4, Minsk 220050, Belarus
Received 26 June 2005; Accepted 1 July 2005
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.
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 whose domain and image are situated in a closed convex
set 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 in some wedges.