Reduction method for functional nonconvex differential inclusions

Year 2021, Volume: 3 Issue: 1, 6 - 14, 29.04.2021

Hanane Chouial , Mustapha Fateh Yarou

https://doi.org/10.47087/mjm.853437

Abstract

Our aim in this paper is to present a reduction method that solves first order functional differential inclusion in the nonconvex case. This approach is based on a discretization of the time interval, a construction of approximate solutions by reducing the problem to a problem without delay and an application of known results in this case. We generalises earlier results, the right hand side of the inclusion has nonconvex values and satisfies a linear growth condition instead to be integrably bounded. The lack of convexity is replaced by the topological properties of decomposable sets, that represents a good alternative in the absence of convexity.

Keywords

delay, linear growth condition, Lower semicontinuous, nonconvex differential inclusion

Supporting Institution

Research supported by the General direction of scientific research and technological development (DGRSDT), Algeria

Project Number

PRFU No. C00L03UN180120180001.

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