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Filippov-Gronwall Inequality for Discontinuous Differential Inclusions

Georgi Smirnov, Francisco Miranda


We prove two versions of the Filippov-Gronwall inequality for differential inclusions with upper semi-continuous right-hand side. The proof of one theorem is based on monotonicity ideas and the other result is deduced from the Kakutani fixed-point theorem. The first theorem is applied to get some sufficient condition of an equilibrium position weak asymptotic stability, and the second one is used to describe tangent vectors to the solution set of a discontinuous differential inclusion.

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