  In this thesis we introduce the concept of a guided dynamical system, and
exploit this idea to solve various problems in functional equations and PDE's.
Our main results are 1) a necessary and sufficient condition for
unique-solvability of an initial value functional equation, 2) a proof of the
overdeterminedness of a large class of functional equations and 3) a necessary
and sufficient condition for unique-solvability of a boundary value problem for
a third order, hyperbolic PDE.
