Fredholm properties of radially symmetric, second order differential operators

Alin Pogan, Arnd Scheel

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)289-327
Number of pages39
JournalInternational Journal of Dynamical Systems and Differential Equations
Volume3
Issue number3
DOIs
StatePublished - Aug 1 2011

Fingerprint

Fredholm Index
Localized Source
Fredholm Property
Morse Index
Implicit Function Theorem
Essential Spectrum
Second-order Systems
Weighted Spaces
Unbounded Domain
Source Terms
Reaction-diffusion System
Chemical Reaction
Linear Operator
Differential operator
Chemical reactions
Bifurcation
Infinity
Perturbation
Calculate
Theorem

Keywords

  • Bifurcation from essential spectrum
  • Differential operators
  • Far-field matching
  • Fredholm properties
  • Radial symmetry

Cite this

Fredholm properties of radially symmetric, second order differential operators. / Pogan, Alin; Scheel, Arnd.

In: International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 3, 01.08.2011, p. 289-327.

Research output: Contribution to journalArticle

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