Approximate Controllability Result for Backward Stochastic Evoluation Inclusions in Hilbert Spaces

Year 2024, Early Access, 1 - 10

Cesim Temel , Müberra Selah

https://doi.org/10.15672/hujms.1487942

Abstract

In this paper, we study semilinear Backward Stochastic Evolution Inclusion systems in Hilbert spaces. First, we prove the existence of mild solution of the semilinear Backward Stochastic Evolution Inclusion systems using a multivalued fixed point theorem. Then, we obtain the approximate controllability result for semilinear Backward Stochastic Evolution Inclusion systems through the linear systems corresponding to these semilinear Backward Stochastic Evolution Inclusion systems under appropriate conditions. In particular, our study extends the results of the concept of approximate controllability to Backward Stochastic Evolution Inclusion systems.

Keywords

Backward Stochastic Evoluation Inclusions, Approximate controllability, Mild solutions, Multivalued maps, Hausdorff measure of noncompactness.

References

• [1] S. Arora and J. Dabas, Existence and approximate controllability of non-autonomous functional impulsive evolution inclusions in Banach spaces, J. Differ. Equ. 307, 83– 113, 2022.