Mathematical Sciences: Critical Point Theory and Differential Equations

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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.