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Differential inclusions with stable subinclusions. (English) Zbl 0816.34011
Using a refinement of Filippov’s theorem for differential inclusions, a singular perturbation problem \[ {x_ 1' \choose \varepsilon x_ 2'} \in F(x_ 1, x_ 2,t) \] for a set-valued map \(F : \mathbb{R}^{n_ 1} \times \mathbb{R}^{n_ 2} \times [0,T] \rightsquigarrow \mathbb{R}^{n_ 1} \times \mathbb{R}^{n_ 2}\) is treated in this paper. Denoting by \(X^ \varepsilon : (0, \varepsilon_ 0) \rightsquigarrow C^{n_ 1} [0,T] \times L_ 2^{n_ 2} [0,T]\) the solution map for a fixed initial condition, the lower semicontinuity of this map at 0 is proved.

MSC:
34A60 Ordinary differential inclusions
34E15 Singular perturbations for ordinary differential equations
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