Nonconvergent radial solutions of a semilinear elliptic equation in R^N
by
Joseph Iaia
University of North Texas

Let u be a bounded radial solution of \Delta u + f(u) = 0 in R^N. Then is it necessarily true lim_{r --> \infty} u(r) exists? For N=2 at least, the answer was shown to be no when in 1994, S. Maier provided a specific nonlinearity f(u) and proved the existence of many nonconvergent solutions for this nonlinearity. Maier also found some necessary conditions on f which must be true in order that there be nonconvergent solutions. In this talk, we improve upon the necessary conditions found by Maier and so are able to rule out the existence of nonconvergent solutions for a wide variety of nonlinearities f(u).

Date received: March 19, 2002