Subcritical bifurcation to infinitely many rotating waves

We consider the equation u '' + (1/r)u' - (k(2)/r(2))u = lambda u + au\u\(2) on r is an element of R+ with k is an element of N, a, lambda is an element of C, Re lambda > 0 > Re a, and \Im lambda\ + \Im a\ < < 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. (C) 1997 Academic Press.