Abstract
In this Chapter a study is made of the equation which is satisfied by an integral funnel (an attainable set) of a differential inclusion which is considered as a multi-function of time. Properties of solutions of this equation are revealed. It is shown that this equation is satisfied not only by the integral funnel of a differential inclusion but also by the integral funnel of an ordinary differential equation having a non-unique solution. An interconnection has been established between solution of the integral funnel equation and solutions of a multi-valued differential equation generated by a differential inclusion. Theorems are formulated for a continuous dependence of the integral funnel on initial conditions and parameters which are distinguished from traditional and known ones in a finite-dimensional space by the absence, in the assumptions, of conditions in explicit form which, with reference to ordinary differential equations, mean uniqueness of the solution.
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