TY - JOUR
T1 - Extremal solutions of differential inclusions via Baire category
T2 - A dual approach
AU - Bressan, Alberto
PY - 2013/10/15
Y1 - 2013/10/15
N2 - Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(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]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).
AB - Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(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]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).
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U2 - 10.1016/j.jde.2013.06.019
DO - 10.1016/j.jde.2013.06.019
M3 - Article
AN - SCOPUS:84881046798
SN - 0022-0396
VL - 255
SP - 2392
EP - 2399
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 8
ER -