  We consider an optimal control problem arising in the context of economic
theory of growth, on the lines of the works by Skiba (1978) and Askenazy - Le
Van (1999).
  The economic framework of the model is intertemporal infinite horizon utility
maximization. The dynamics involves a state variable representing total
endowment of the social planner or average capital of the representative
dynasty. From the mathematical viewpoint, the main features of the model are
the following: (i) the dynamics is an increasing, unbounded and not globally
concave function of the state; (ii) the state variable is subject to a static
constraint; (iii) the admissible controls are merely locally integrable in the
right half-line. Such assumptions seem to be weaker than those appearing in
most of the existing literature.
  We give a direct proof of the existence of an optimal control for any initial
value of the state variable and we carry on a qualitative study of the value
function; moreover, using dynamic programming methods, we show that the value
function is a continuous viscosity solution of the associated
Hamilton-Jacobi-Bellman equation.
