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#### References

- Albeverio, S.; Mandrekar, V.; Rüdiger, B. Existence of mild solutions for stochastic differential equations and
semilinear equations with non-Gaussian Lévy noise.
*Stochastic Process. Appl.*119 (2009), no. 3, 835--863. MR2499860 - Burton, T. A. Stability by fixed point theory or Liapunov theory: a comparison.
*Fixed Point Theory*4 (2003), no. 1, 15--32. MR2031819 - Burton, T. A. Fixed points, stability, and exact linearization.
*Nonlinear Anal.*61 (2005), no. 5, 857--870. MR2130068 - Burton, T. A.; Furumochi, Tetsuo. Asymptotic behavior of solutions of functional differential equations
by fixed point theorems.
*Dynam. Systems Appl.*11 (2002), no. 4, 499--519. MR1946140 - Burton, T. A.; Zhang, Bo. Fixed points and stability of an integral equation: nonuniqueness.
*Appl. Math. Lett.*17 (2004), no. 7, 839--846. MR2072844 - Chow, Pao Liu. Stability of nonlinear stochastic-evolution equations.
*J. Math. Anal. Appl.*89 (1982), no. 2, 400--419. MR0677738 - Caraballo, Tomás; Real, José. Partial differential equations with delayed random perturbations:
existence, uniqueness, and stability of solutions.
*Stochastic Anal. Appl.*11 (1993), no. 5, 497--511. MR1243598 - Caraballo, Tomás; Liu, Kai. Exponential stability of mild solutions of stochastic partial
differential equations with delays.
*Stochastic Anal. Appl.*17 (1999), no. 5, 743--763. MR1714897 - Cui, Jing; Yan, Litan; Sun, Xichao. Exponential stability for neutral stochastic partial differential
equations with delays and Poisson jumps.
*Statist. Probab. Lett.*81 (2011), no. 12, 1970--1977. MR2845915 - Hernández M, Eduardo; Henríquez, Hernán R.; dos Santos, José Paulo C. Existence results for abstract partial neutral integro-differential
equation with unbounded delay.
*Electron. J. Qual. Theory Differ. Equ.*2009, No. 29, 23 pp. MR2501417 - Kolmanovskiĭ, V.; Myshkis, A. Applied theory of functional-differential equations.
Mathematics and its Applications (Soviet Series), 85.
*Kluwer Academic Publishers Group, Dordrecht,*1992. xvi+234 pp. ISBN: 0-7923-2013-1 MR1256486 - Kuang, Yang. Delay differential equations with applications in population
dynamics.
Mathematics in Science and Engineering, 191.
*Academic Press, Inc., Boston, MA,*1993. xii+398 pp. ISBN: 0-12-427610-5 MR1218880 - Liu, Kai; Truman, Aubrey. A note on almost sure exponential stability for stochastic partial
functional differential equations.
*Statist. Probab. Lett.*50 (2000), no. 3, 273--278. MR1792306 - Luo, Jiaowan. Fixed points and stability of neutral stochastic delay differential
equations.
*J. Math. Anal. Appl.*334 (2007), no. 1, 431--440. MR2332567 - Luo, Jiaowan. Fixed points and exponential stability of mild solutions of stochastic
partial differential equations with delays.
*J. Math. Anal. Appl.*342 (2008), no. 2, 753--760. MR2433617 - Luo, Jiaowan; Taniguchi, Takeshi. Fixed points and stability of stochastic neutral partial differential
equations with infinite delays.
*Stoch. Anal. Appl.*27 (2009), no. 6, 1163--1173. MR2573454 - Liu, Kai. Stability of infinite dimensional stochastic differential equations
with applications.
Chapman & Hall/CRC Monographs and Surveys in Pure and Applied
Mathematics, 135.
*Chapman & Hall/CRC, Boca Raton, FL,*2006. xii+298 pp. ISBN: 978-1-58488-598-6; 1-58488-598-X MR2165651 - Liu, Kai; Truman, Aubrey. Moment and almost sure Lyapunov exponents of mild solutions of
stochastic evolution equations with variable delays via approximation
approaches.
*J. Math. Kyoto Univ.*41 (2001), no. 4, 749--768. MR1891673 - Nunziato, Jace W. On heat conduction in materials with memory.
*Quart. Appl. Math.*29 (1971), 187--204. MR0295683 - Pazy, A. Semigroups of linear operators and applications to partial differential
equations.
Applied Mathematical Sciences, 44.
*Springer-Verlag, New York,*1983. viii+279 pp. ISBN: 0-387-90845-5 MR0710486 - Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions.
Encyclopedia of Mathematics and its Applications, 44.
*Cambridge University Press, Cambridge,*1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136 - Taniguchi, Takeshi. The exponential stability for stochastic delay partial differential
equations.
*J. Math. Anal. Appl.*331 (2007), no. 1, 191--205. MR2305998 - Taniguchi, Takeshi; Luo, Jiaowan. The existence and asymptotic behaviour of mild solutions to stochastic
evolution equations with infinite delays driven by Poisson jumps.
*Stoch. Dyn.*9 (2009), no. 2, 217--229. MR2531628 - Wang, Feng-Yu; Zhang, Tu-Sheng. Gradient estimates for stochastic evolution equations with
non-Lipschitz coefficients.
*J. Math. Anal. Appl.*365 (2010), no. 1, 1--11. MR2585069 - Xu, Tiange; Zhang, Tusheng. White noise driven SPDEs with reflection: existence, uniqueness and
large deviation principles.
*Stochastic Process. Appl.*119 (2009), no. 10, 3453--3470. MR2568282

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