  We consider a nonlinear optimal control problem governed by a nonlinear
evolution inclusion and depending on a parameter $\lambda$. First we examine
the dynamics of the problem and establish the nonemptiness of the solution set
and produce continuous selections of the solution multifunction $\xi\mapsto
S(\xi)$ ($\xi$ being the initial condition). These results are proved in a very
general framework and are of independent interest as results about evolution
inclusions. Then we use them to study the sensitivity properties of the optimal
control problem. We show that we have Hadamard well-posedness (continuity of
the value function) and we establish the continuity properties of the optimal
multifunction. Finally we present an application on a nonlinear parabolic
distributed parameter system.
