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Nonlinear impulsive systems on infinite dimensional spaces. (English) Zbl 1030.34056
Summary: The authors consider two different classes of nonlinear impulsive systems one driven purely by Dirac measures at a fixed set of points and the second driven by signed measures. The later class is easily extended to systems driven by general vector measures. The principal nonlinear operator is monotone hemicontinuous and coercive with respect to certain triple of Banach spaces called Gelfand triple. The other nonlinear operators are more regular, nonmonotone continuous operators with respect to suitable Banach spaces.
We present here a new result on the compact embedding of the space of vector-valued functions of bounded variation and then use this result to prove two new results on existence and regularity properties of solutions for impulsive systems described above. The new embedding result covers the well-known embedding result due to Aubin.

34G20 Nonlinear differential equations in abstract spaces
34K45 Functional-differential equations with impulses
34A37 Ordinary differential equations with impulses
46G10 Vector-valued measures and integration
47J35 Nonlinear evolution equations
Full Text: DOI
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