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March  2018, 8(1): 81-95. doi: 10.3934/naco.2018005

## Unbounded state-dependent sweeping processes with perturbations in uniformly convex and q-uniformly smooth Banach spaces

 1 XLIM UMR-CNRS 7252, Université de Limoges, 87060 Limoges, France 2 Centro de Modelamiento Matemático (CMM), Universidad de Chile, Santiago, Chile

* Corresponding author

Received  December 2016 Revised  January 2018 Published  March 2018

Fund Project: The second author is supported by Fondecyt Postdoc Project 3150332.

In this paper, the existence of solutions for a class of first and second order unbounded state-dependent sweeping processes with perturbation in uniformly convex and $q$-uniformly smooth Banach spaces are analyzed by using a discretization method. The sweeping process is a particular differential inclusion with a normal cone to a moving set and is of a great interest in many concrete applications. The boundedness of the moving set, which plays a crucial role for the existence of solutions in many works in the literature, is not necessary in the present paper. The compactness assumption on the moving set is also improved.

Citation: Samir Adly, Ba Khiet Le. Unbounded state-dependent sweeping processes with perturbations in uniformly convex and q-uniformly smooth Banach spaces. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 81-95. doi: 10.3934/naco.2018005
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