This project will involve the study of various variational problems in dynamical systems and partial differential equations. The basic problems studied include (a) three and n-body type problems, (b) the Weinstein conjecture, which concerns periodic orbits on odd-dimensional compact manifolds, (c) the existence of solutions to superlinear elliptic problems, and (d) elliptic variational problems involving the critical Sobolev exponent, including problems on contractible domains and curvature problems. In addition to making contributions in the areas of partial differential equations and differential geometry, this work can be applied to dynamical systems and potential theory.
