Abstract and Applied Analysis
Volume 2011 (2011), Article ID 629692, 21 pages
http://dx.doi.org/10.1155/2011/629692
Research Article

Properness and Topological Degree for Nonlocal Reaction-Diffusion Operators

N. Apreutesei1 and V. Volpert2

1Department of Mathematics, “Gh. Asachi” Technical University of Iasi, Bd. Carol. I, 700506 Iasi, Romania
2Institut Camille Jordan, UMR 5208 CNRS, Université Lyon 1, 69622 Villeurbanne, France

Received 5 December 2010; Accepted 25 February 2011

Academic Editor: Nobuyuki Kenmochi

Copyright © 2011 N. Apreutesei and V. Volpert. 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.

Abstract

The paper is devoted to integro-differential operators, which correspond to nonlocal reaction-diffusion equations considered on the whole axis. Their Fredholm property and properness will be proved. This will allow one to define the topological degree.