Critical Point Theory and Differential Equations

作者：postmaster at nsf 1日期： 1998年3月11日下午4：37优先级：正常收件人：cberenst at nsf 11主题：Bahri摘要- 本文旨在研究偏微分方程中的各种变分问题 微分方程和接触形式几何。 这些问题 与Yamabe型变号解的研究有关 问题以及杨米尔斯和爱因斯坦方程的研究。 它们也与发现接触的周期轨道有关 向量场 最后，它与量子力学有某种联系。 这些工具是从偏微分方程，几何 变分理论。 \medskip 在物理学中有几个关于形状和形状的悬而未决的问题。 宇宙的行为以及它的基本行为 粒子 利用这些数学、变分理论和 特别是它的扩展，我们试图做出一些贡献， 对这些问题的理解，这有一个独立的 数学兴趣 \end

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