Nonlinear impulsive systems on infinite dimensional spaces |
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| Institution: | 1. Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Egypt;2. Department of Basic Sciences, Deanship of Preparatory Year and Supporting Studies, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia;3. Engineering Mathematics and Physics Department, Cairo University, 12613, Egypt;4. Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt;1. Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402-6170, USA;2. Department of Mathematics, Winston-Salem State University, 148 Carolina Hall, Winston-Salem, NC 27110 USA |
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| Abstract: | In this paper we 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, 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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