It is the purpose of this paper
to study multidimensional nonlinear integral equations of Volterra type of a
rather general form with unknowns in one of the function spaces C,L1,L∞ or
Lp,1 < p < +∞. In analogy with the theory of differential equations, global existence
and uniqueness theorems as well as continuous dependence on initial values, are
established for such integral equations. The hypotheses on integrands in this paper
are less demanding than normally found in the literature and are motivated by
applications, particularly to boundary value problems found in optimal control
theory.
