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Nonlinear impulsive systems on infinite dimensional spaces

✍ Scribed by N.U. Ahmed; K.L. Teo; S.H. Hou

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
191 KB
Volume
54
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper we consider two di erent classes of nonlinear impulsive systems one driven purely by Dirac measures at a ΓΏxed 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, non-monotone continuous operators with respect to suitable Banach spaces. We present here a new result on 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.

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The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on R n failing