Remark on the Bellman equation for optimal control problems with exit times and noncoercing dynamics

This study is a continuation of a work on uniqueness questions for viscosity solutions of Hamilton-Jacobi-Bellman equations (HJB\u27s) arising from deterministic control problems with exit times. A general uniqueness theorem is proven that characterizes the value functions for a class of problems of this type for nonlinear systems as the unique solutions of the corresponding HJBs among continuous functions with appropriate boundary conditions when the dynamical law is non-Lipschitz and noncoercing