Title: Fredholm properties of radially symmetric, second order differential operators

Authors: Alin Pogan, Arnd Scheel

Addresses: School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA. ' School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA

Abstract: We analyse Fredholm properties of radially symmetric second order systems in unbounded domains. The main theorem relates the Fredholm index to the Morse index at infinity. As a consequence, linear operators are Fredholm in exponentially weighted spaces for almost all weights. The result provides the basic tool for the analysis of perturbation and bifurcation problems in the presence of essential spectrum. We give a simple illustrative example, where we use the implicit function theorem to calculate the effect of a localised source term on a trimolecular chemical reaction-diffusion systems on the plane.

Keywords: differential operators; Fredholm properties; radial symmetry; bifurcation; essential spectrum; far-field matching; trimolecular chemical reaction-diffusion systems.

DOI: 10.1504/IJDSDE.2011.041878

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.3, pp.289 - 327

Published online: 24 Jan 2015 *

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