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 language | English (US) |
|---|---|
| Pages (from-to) | 289-327 |
| Number of pages | 39 |
| Journal | International Journal of Dynamical Systems and Differential Equations |
| Volume | 3 |
| Issue number | 3 |
| DOIs | |
| State | Published - Aug 1 2011 |
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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 journal › Article
}
TY - JOUR
T1 - Fredholm properties of radially symmetric, second order differential operators
AU - Pogan, Alin
AU - Scheel, Arnd
PY - 2011/8/1
Y1 - 2011/8/1
N2 - 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.
AB - 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.
KW - Bifurcation from essential spectrum
KW - Differential operators
KW - Far-field matching
KW - Fredholm properties
KW - Radial symmetry
UR - http://www.scopus.com/inward/record.url?scp=80051731833&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051731833&partnerID=8YFLogxK
U2 - 10.1504/IJDSDE.2011.041878
DO - 10.1504/IJDSDE.2011.041878
M3 - Article
AN - SCOPUS:80051731833
VL - 3
SP - 289
EP - 327
JO - International Journal of Dynamical Systems and Differential Equations
JF - International Journal of Dynamical Systems and Differential Equations
SN - 1752-3583
IS - 3
ER -