A Favard type theorem for Hurwitz polynomials
Multiplicity results for fourth order problems related to the theory of deformations beams
February 2020, 25(2): 507-528. doi: 10.3934/dcdsb.2019251
Existence and exponential stability for neutral stochastic integro–differential equations with impulses driven by a Rosenblatt process
Tomás Caraballo 1, , Carlos Ogouyandjou 2, , Fulbert Kuessi Allognissode 2, and Mamadou Abdoul Diop 3,
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012-Sevilla, Spain
Université d'Abomey-Calavi(UAC), Institut de Mathématiques et de Sciences Physiques(IMSP), 01 B.P. 613, Porto-Novo, République du Bénin
Université Gaston Berger de Saint-Louis, UFR SAT Département de Mathématiques, B.P234, Saint-Louis, Sénégal
Dedicated to Prof. Dr. Juan J. Nieto on the occasion of his 60th birthday
Received January 2019 Revised March 2019 Published November 2019
Fund Project: This work has been partially supported by FEDER and the Spanish Ministerio de Economía y Competitividad project MTM2015-63723-P and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under Proyecto de Excelencia P12-FQM-1492.
The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed in this work by using the Banach fixed point theorem and the theory of resolvent operator developed by R. Grimmer in [12]. Furthermore, the exponential stability in mean square for the mild solution to neutral stochastic integro–differential equations with Rosenblatt process is obtained by establishing an integral inequality. Finally, an example is exhibited to illustrate the abstract theory.
Keywords: Exponential stability, resolvent operator, impulsive neutral stochastic integro–differential equations, Rosenblatt process.
Mathematics Subject Classification: 60H15, 35R60.
Citation: Tomás Caraballo, Carlos Ogouyandjou, Fulbert Kuessi Allognissode, Mamadou Abdoul Diop. Existence and exponential stability for neutral stochastic integro–differential equations with impulses driven by a Rosenblatt process. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 507-528. doi: 10.3934/dcdsb.2019251
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Tomás Caraballo Carlos Ogouyandjou Fulbert Kuessi Allognissode Mamadou Abdoul Diop