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Integral estimates for ordinary differential equations and their application to nonsmooth optimal control problems. (Russian) Zbl 0762.34015
Two integral estimates are derived for the solution of the ordinary differential equation $$\dot y(t)=f(y(t),t)$$, $$t\in[0,T]$$. The estimates are utilized in the problem of nonsmooth optimal control with a random initial state $$y(0)=a$$. Existence theorems for optimal control solutions are derived.
Reviewer: J.Ramik (Ostrava)

##### MSC:
 34C11 Growth and boundedness of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory 49J15 Existence theories for optimal control problems involving ordinary differential equations