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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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Fredholm Alternative for the p-Laplacian II
by
Petr Girg
Centre of Applied Mathematics, University of West Bohemia, Plzen, Czech Republic
Coauthors: Marek Brandner (University of West Bohemia), Jan Cepicka (University of West Bohemia), Pavel Drabek (University of West Bohemia), Jose Luis Gamez (University of Granada), Raul Manasevich (University of Chile), Peter Takac (University of Rostock), Michael Ulm (University of Rostock)

We shall apply the bifurcation type argument to the behaviour of the solution pairs \lambda in R, u in W1, p0(\Omega) of
\labeleqone-\Deltap u-\lambda|u|p-2u=f in \Omega     u=0 on \partial\Omega ,
(\theequation)
when \lambda --> \lambda1 and ||u|| --> \infty. Existence and multiplicity results for () are derived from here. In the new light of results obtained by bifurcation-type arguments, we revise previous results obtained by combination of the method of upper and lower solutions and variational approach.

We will also emphasize importance of the interplay between numerical experiment and development of new theoretical methods on one hand, and theoretical results and development of new numerical methods on the other hand. Finally, we would like to discuss several directions of future research and some open problems as well. This talk will be predominatly both theoretical and computational.

Date received: March 28, 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-08.