Some Problems in Nonlinear Analysis
Final rept. 23 May 1987-22 May 1990
Pagination or Media Count:
Crandall has worked on several questions including applications of nonlinear semigroup theory to nonlinear diffusion problems, the abstract theory of evolution equations, the theoretical basis for Hamilton Jacobi equations in infinite dimensions and its application to dynamic programming in infinite dimensional control and differential games, and the theory of viscosity solutions of fully nonlinear second order partial differential equations. Rabinowitz has worked on a variety of problems which have the common feature that they all involve the development of methods in the calculus of variations and their application to differential equations. In particular he treated the existence of periodic solutions of smooth Hamiltonian systems and systems involving singular potentials, the existence of various types of connecting orbits of Hamiltonian systems such as homoclinic and heteroclinic solutions, and the existence of multiple solutions of semilinear elliptic equations.
- Theoretical Mathematics