Mild solutions of local non-Lipschitz neutral stochastic partial functional differential equations
This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation with in-nite delays using Caratheodory conditions and also the exponential stability of the moments of a mild solutions well as its sample paths.
An example is provided to illustrate the obtained result.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, NY, USA, (1983).
A.E. Rodkina, On existence and uniquness of solution of stochastic differential equations with heredity, Stochastic 12, 187-200, (1984).
G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge, (1992).
J. Luo, Stability of stochastic partial differential equations with infinite delays, Journal of Computational and Applied Mathematics, 222, 364-371, (2008).
M. He, Global Existence and Stability of Solution for Reaction Diffusion Functional Differential Equations J. Math. Anal. Appl. 199, 842-858, (1996).
Nan Ding, Exponential Stability in Mean Square for Neutral Stochastic Partial Functional Differential Equations with Impulses, Journal of Applied Mathematics Volume Article ID 729159, 8 pages, (2013).
N. U. Ahmed, Semigroup Theory with Applications to Systems and Control, vol. 246 of Pitman Research Notes in Mathematics Series, Longman Scientic and Technical, Harlow, UK, (1991).
T.E. Govindan, Stability of mild solutions of stochastic evolution equations with variable delays, Stoch. Anal Appl. 21, 1059-1077, (2003).
T. E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics, vol. 77, no. 2, pp. 139154, (2005).
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