Subcritical bifurcation to infinitely many rotating waves

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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.

Original languageEnglish (US)
Pages (from-to)252-261
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Nov 1 1997
Externally publishedYes


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