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Seventh Mississippi State - UAB Conference on Differential Equations & Computational Simulations
November 1-3, 2007
Doubletree Hotel
Birmingham, AL, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Finite Morse Index Solutions and the Branch of Positive Solutions of Exponential Problems
by
E. N. Dancer
School of Mathematics and Statistics, University of Sydney

We discuss the recent proof that the branch of positive solutions of - Du = r eu in D, u=0 on the boundary of D starting from (0, 0) has infinitely many bifurcation points.Here D is a bounded smooth 3-dimensional domain.This generalises to general domains results only known for the ball and the annulus. We also discuss the generalisation to N dimensional domains for N between 3 and 9 (joint work with Dupaigne and Farina) and the two key ingredients in the proof: real analytic bifurcation theory and finite Morse index solutions of our equation on the whole space.We also briefly discuss corresponding results for nonlinearities asymptotically a supercritical power.

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Date received: August 15, 2007

Copyright © 2007 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 # cauf-13.