Topological method for coupled systems of impulsive stochastic semilinear differential inclusions with fractional Brownian motion


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	Topological method for coupled systems of impulsive stochastic semilinear differential inclusions with fractional Brownian motion


	Fixed Point Theory, Volume 20, No. 1, 2019, 71-106, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.05 Authors: T. Blouhi, T. Caraballo and A. Ouahab Abstract: In this paper we prove the existence of mild solutions for a first-order impulsive semilinear stochastic differential inclusion with an infinite-dimensional fractional Brownian motion. We consider the cases in which the right hand side can be either convex or nonconvex-valued. The results are obtained by using two different fixed point theorems for multivalued mappings, more precisely, the technique is based on a multivalued version of Perov's fixed point theorem and a new version of a nonlinear alternative of Leray-Schauder's fixed point theorem in generalized Banach spaces. Key Words and Phrases: Mild solutions, fractional Brownian motion, impulses, matrix convergent to zero, generalized Banach space, fixed point, set-valued analysis, differential inclusions. 2010 Mathematics Subject Classification: 34A37, 60H15, 60H20, 47H10. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents