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Filippov's Operator And Discontinuous Differential Equations, Khalid Abdulaziz Alshammari
Filippov's Operator And Discontinuous Differential Equations, Khalid Abdulaziz Alshammari
LSU Doctoral Dissertations
The thesis is mainly concerned about properties of the so-called Filippov operator that is associated with a differential inclusion x'(t) ε F(x(t)) a.e. t ε [0,T], where F : Rn → Rn is given set-valued map. The operator F produces a new set-valued map F[F], which in effect regularizes F so that F[F] has nicer properties. After presenting its definition, we show that F[F] is always upper-semicontinuous as a map from Rn to the metric space of compact subsets of Rn endowed with the Hausdorff metric. Our main approach is to study the …