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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

CONLEY INDEX AND HOMOLOGY INDEX BRAIDS IN SINGULAR PERTURBATION PROBLEMS WITHOUT UNIQUENESS OF SOLUTIONS

Author(s):
Carbinatto, Maria C. [1] ; Rybakowski, Krzysztof P. [2]
Total Authors: 2
Affiliation:
[1] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Rostock, Inst Math, D-18057 Rostock - Germany
Total Affiliations: 2
Document type: Journal article
Source: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 35, n. 1, p. 1-32, MAR 2010.
Web of Science Citations: 0
Abstract

We define the concept of a Conley index and a homology index braid class for ordinary differential equations of the form (E) x = F(1)(x), where M is a C(2)-manifold and F(1) is the principal part of a continuous vector field on M This allows us to extend our previously obtained results from {[}5] on singularly perturbed systems of ordinary differential equations epsilon y = f(y, x, epsilon), (E(epsilon)) x = h(y, x, epsilon) on Y x M, where Y is a finite dimensional Banach space and M is a C(2)- manifold. to the case where the vector field in (E(epsilon)) is continuous, but not necessarily locally Lipschitzian (AU)