Critical Point Theory and Differential Equations

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Author: postmaster at nsf1 Date: 3/11/98 4:37 PM Priority: Normal TO: cberenst at nsf11 Subject: Abstract for Bahri ------------------------------- Message Contents ------------------------------- Abbas Bahri This proposal aims at studying various variational problems in Partial Differential Equations and contact form geometry. These problems are connected to the study of changing sign solutions for Yamabe type problems as well as the study of Yang-Mills and Einstein equations. They are also connected to the finding of periodic orbits for contact vector fields. There is finally some relation to quantum mechanics. The tools are extracted from partial differential equations, geometry and variational theory. \medskip There are in Physics several open problems regarding the shape and the behavior of the universe as well as the behavior of its elementary particles. Using these tools from mathematics, variational theory and its extensions in particular, we are trying to give some contribution to the understanding of these problems, which have an independent mathematical interest. \end