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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA

Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)

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Newton's Method, Morse Index, and Bifurcation of Solutions to Semilinear Elliptic BVP
by
John Neuberger
Northern Arizona University
Coauthors: Jim Swift

We consider a semilinear elliptic Dirichlet problem and seek to find solutions as critical points of a variational functional. Since such solutions are saddle points, one needs constraints in order to find these solutions as minimax. Following our recent existence results of certain sign-changing solutions, we developed a numerical method based on Newton's method which uses Eigenfunction expansions in order to find many solutions of arbitrary Morse index. We find these solutions to lie on various primary, secondary, and tertiary bifurcation curves.

Date received: April 17, 1999

Copyright © 1999 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 # cacr-73.