Extremal Solutions of Differential Inclusions via Baire Category: a Dual Approach
نویسنده
چکیده
Let F be a continuous multifunction on IR with compact convex values. For any vector w, let F(x) ⊆ F (x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w : [0, T ] 7→ IR with the following property: all solutions to the Cauchy problem ẋ(t) ∈ F(x(t)), x(0) = 0, are also solutions to ẋ(t) ∈ extF (x(t)). We prove that W is residual in C([0, T ]; IR).
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