  The solution existence of finite horizon optimal economic growth problems is
studied by invoking Filippov's Existence Theorem for optimal control problems
with state constraints of the Bolza type from the monograph of L. Cesari
[Optimization Theory and Applications, Springer-Verlag, New York, 1983]. Our
results are obtained not only for general problems but also for typical ones
with the production function and the utility function being either the AK
function or the Cobb--Douglas one. Some open questions and conjectures about
the regularity of the global solutions of finite horizon optimal economic
growth problems are formulated in this paper.
