Stability results for neutral stochastic functional differential equations via fixed point methods

References

• Appleby, J. A. D. (2008). Fixed points, stability and harmless stochastic perturbations. Preprint.
   Google Scholar
• Burton, T. A. (2004). Fixed points and stability of a nonconvolution equation. Proceedings of the American Mathematical Society, 132, 3679–3687. doi: 10.1090/S0002-9939-04-07497-0
   Web of Science ®Google Scholar
• Burton, T. A. (2005). Fixed points, stability, and exact linearization. Nonlinear Analysis: Theory, Methods & Applications, 61, 857–870. doi: 10.1016/j.na.2005.01.079
   Web of Science ®Google Scholar
• Burton, T. A. (2006). Stability by fixed point theory for functional differential equations. Mineola, NY: Dover.
   Google Scholar
• Burton, T. A., & Zhang, B. (2004). Fixed points and stability of an integral equation: Nonuniqueness. Applied Mathematics Letters, 17, 839–846. doi: 10.1016/j.aml.2004.06.015
   Web of Science ®Google Scholar
• Dib, Y. M., Maroun, M. R., & Raffoul, Y. N. (2005). Periodicity and stability in neutral nonlinear differential equations with functional delay. Electronic Journal of Differential Equations, 2005(142), 1–11.
   Google Scholar
• Guo, Y., Xu, C., & Wu, J. (2017). Stability analysis of neutral stochastic delay differential equations by a generalisation of Banach's contraction principle. International Journal of Control, 90, 1555–1560. doi: 10.1080/00207179.2016.1213524
   Web of Science ®Google Scholar
• Karatzas, I., & Shreve, S. E. (1991). Brownian motion and stochastic calculus (2nd ed.). Vol. 113 of graduate texts in mathematics. New York, NY: Springer.
   Google Scholar
• Luo, J. W. (2007). Fixed points and stability of neutral stochastic delay differential equations. Journal of Mathematical Analysis and Applications, 334, 431–440. doi: 10.1016/j.jmaa.2006.12.058
   Web of Science ®Google Scholar
• Luo, J. W. (2008). Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays. Journal of Mathematical Analysis and Applications, 342, 753–760. doi: 10.1016/j.jmaa.2007.11.019
   Web of Science ®Google Scholar
• Luo, J. W. (2010). Fixed points and exponential stability for stochastic Volterra-Levin equations. Journal of Computational and Applied Mathematics, 234, 934–940. doi: 10.1016/j.cam.2010.02.013
   Web of Science ®Google Scholar
• Pinto, M., & Sepúlveda, D. (2011). H-asymptotic stability by fixed point in neutral nonlinear differential equations with delay. Nonlinear Analysis: Theory, Methods & Applications, 74, 3926–3933. doi: 10.1016/j.na.2011.02.029
   Web of Science ®Google Scholar
• Raffoul, Y. N. (2004). Stability in neutral nonlinear differential equations with functional delays using fixed-point theory. Mathematical and Computer Modelling, 40, 691–700. doi: 10.1016/j.mcm.2004.10.001
   Google Scholar
• Sakthivel, R., & Luo, J. W. (2009a). Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. Journal of Mathematical Analysis and Applications, 356, 1–6. doi: 10.1016/j.jmaa.2009.02.002
   Web of Science ®Google Scholar
• Sakthivel, R., & Luo, J. W. (2009b). Asymptotic stability of nonlinear impulsive stochastic differential equations. Statistics and Probability Letters, 79, 1219–1223. doi: 10.1016/j.spl.2009.01.011
   Web of Science ®Google Scholar
• Smart, D. R. (1974). Fixed point theorems. Cambridge tracts in mathematics; No. 66. London,NY: Cambridge University Press.
   Google Scholar
• Zhang, B. (2004). Contraction mapping and stability in a delay differential equation. Dynamical Systems and Applications, 4, 183–190.
   Google Scholar
• Zhang, B. (2005). Fixed points and stability in differential equations with variable delays. Nonlinear Analysis: Theory, Methods & Applications, 63, e233–e242. doi: 10.1016/j.na.2005.02.081
   Web of Science ®Google Scholar
• Zhou, X., & Zhong, S. (2010). Fixed point and exponential p-stability of neutral stochastic differential equations with multiple delays. In Proceedings of the 2010 IEEE international conference on intelligent computing and intelligent systems, Liverpool, UK (pp. 1238–1242). ICIS. Art. no. 5658577.
   Google Scholar