(I) Control problems optimal for deterministic control systems: (controls with compact and/or unlimited values; impulsive) existence of optimal control; uniqueness of the solution of the associated HJ equation in the sense of viscosity; necessary optimality conditions(maximum principle) and nonsmooth analysis

(II) Asymptotic controllability, stabilizability and Control-Lyapunov functions: for optimal control problems with exit time. Applications to study the regularity of the associated value function and the stability of the associated HJ equation;

(III) Control problems optimal for stochastic control systems: (controls with compact and/or singular values) existence of the optimal control; uniqueness of the solution of the associated HJ equation in the sense of viscosity;

(IV) Existence of the solution for systems of Hamilton-Jacobi "multi-time"; equations, i. e. systems of N Hamilton-Jacobi equations, each evolving with respect to a different time.