TY - JOUR
T1 - Subcritical bifurcation to infinitely many rotating waves
AU - Scheel, Arnd
PY - 1997/11/1
Y1 - 1997/11/1
N2 - We consider the equationu″+(1/r)u′-(k2/r2)u=λu+au|u|2onr∈R+withk∈N,a, λ∈C, Reλ0Rea, and |Imλ|+|Ima|<<1. Bounded solutions possess an interesting interpretation as rotating wave solutions to reaction-diffusion systems in the plane. Our main results claim that there are countably many solutions which are decaying to zero at infinity. The proofs rely on nodal properties of the equation and a Melnikov analysis.
AB - We consider the equationu″+(1/r)u′-(k2/r2)u=λu+au|u|2onr∈R+withk∈N,a, λ∈C, Reλ0Rea, and |Imλ|+|Ima|<<1. Bounded solutions possess an interesting interpretation as rotating wave solutions to reaction-diffusion systems in the plane. Our main results claim that there are countably many solutions which are decaying to zero at infinity. The proofs rely on nodal properties of the equation and a Melnikov analysis.
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U2 - 10.1006/jmaa.1997.5651
DO - 10.1006/jmaa.1997.5651
M3 - Article
AN - SCOPUS:0031260793
SN - 0022-247X
VL - 215
SP - 252
EP - 261
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -