Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Mönch fixed point

By Sufang Deng, Xiao-Bao Shu, J. Mao. Journal of Mathematical Analysis and Applications, 2018

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Abstract In this paper, we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup in Hilbert spaces. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Monch fixed point theorem. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

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