Mathematical Sciences: Critical Point Theory and Differential Equations

Bahri将研究动力系统、非线性偏微分方程和几何中出现的问题。这些问题包括三体型上的碰撞和周期轨道的存在性，给定能量表面上无限多椭圆轨道和无限多双曲轨道的存在性，温斯坦猜想和接触形式的伪轨道，以及超线性椭圆问题。偏微分方程是物理世界数学建模的基础。数学分析的作用与其说是创建方程，不如说是提供关于解的定性和定量信息。这可能包括回答关于独特性、平滑性和增长性的问题。此外，分析常常发展出解的近似方法和对这些近似精度的估计。

PI: Bahri DMS-9501132 Bahri will investigate questions arising in dynamical systems, nonlinear partial differential equations and geometry. These include collisions and existence of periodic orbits on 3-body type, the existence of infinitely many elliptic and infinitely many hyperbolic orbits on a given energy surface, the Weinstein conjecture and pseudo-orbits of contact forms, and the superlinear elliptic problem. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.