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The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.
A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).
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