Further results on the Bellman equation for exit time optimal control problems with nonnegative Lagrangians: The case of Fuller\u27s problem

In this study, an attempt is made to prove that the value function for a class of problems including Fuller\u27s Problem is the unique viscosity solution of the Bellman equation that vanishes at the target and is bounded below. The study uses the fact that all trajectories of these problems tend to a given origin