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Existence, uniqueness, and stability of stochastic neutral functional differential equations of Sobolev-type

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.4936647· OSTI ID:22479571
;  [1]
  1. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, Jiangsu (China)
In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii’s fixed point theorem, respectively. Furthermore, we use the Bihari’s inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the Gronwall inequality. Finally, two examples are given to illustrate the theory results.
OSTI ID:
22479571
Journal Information:
Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 56; ISSN JMAPAQ; ISSN 0022-2488
Country of Publication:
United States
Language:
English

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