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Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms
June 5-8, 2002
Northern Arizona University
Flagstaff, AZ, USA

Organizers
John M. Neuberger, NAU, James W. Swift, NAU, Ratnasingham, Shivaji, MSU

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Nonconvergent radial solutions of a semilinear elliptic equation in RN
by
Joseph Iaia
University of North Texas

Let u be a bounded radial solution of \Delta u + f(u) = 0 in RN. Then is it necessarily true limr --> \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

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caio-06.