Subcritical Bifurcation to Innnitely Many Rotating Waves

@inproceedings{Scheel2007SubcriticalBT,
  title={Subcritical Bifurcation to Innnitely Many Rotating Waves},
  author={Arnd Scheel},
  year={2007}
}
We consider the equation u00 + 1 ru0 k2 r2 u = u + aujuj2 on r 2 R+ with k 2 N, a; 2 C , Re > 0 > Re a, and j Im j+ j Imaj << 1. Bounded solutions possess an interesting interpretation as rotating wave solutions to reaction-di usion systems in the plane. Our main results claim that there are countably many solutions which are decaying to zero at in nity. The proofs rely on nodal properties of the equation and a Melnikov analysis. 2 

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