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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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Newton's Method and Bifurcation of Solutions for Nonlinear Elliptic PDE.
by
John M. Neuberger
Northern Arizona University

We consider semilinear elliptic PDE of the form \Delta u + f(u) = 0 on piecewise smooth bounded regions \Omega in RN, with appropriate boundary conditions. Under specific assumptions on the nonlinearity f, much is known about the existence, multiplicity, and nodal structure of solutions to the PDE, but still much more remains to be proven. We present an algorithm of Neuberger and Swift for approximating solutions to a large class of variational problems, and discuss the results of many numerical investigations by Neuberger and students of Neuberger. In particular, we investigate bifurcation of solutions from primary branches as problem-dependent parameters vary.

Date received: November 27, 2001

Copyright © 2001 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-02.