Second-order neutral impulsive stochastic evolution equations with infinite daelay

Hino Y, Murakami S, Naito T Lecture Notes in Mathematics 1473. In Functional Differential Equations with Infinite Delay. Springer, Berlin; 1991.

Caraballo T: Asymptotic exponential stability of stochastic partial differential equationswith delay. Stochastics 1990, 33: 27–47.

Da Prato G, Zabczyk J: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge; 1992.

Mahmudov NI: Existence and uniqueness results for neutral SDEs in Hilbert spaces. Stoch. Anal. Appl. 2006, 24: 79–95. 10.1080/07362990500397582

Mao X: Stochastic Differential Equations and Applications. Horwood, Chichester; 1997.

Hale JK, Lunel SMV: Introduction to Functional Differential Equations. Springer, Berlin; 1991.

Kolmanovskii VB, Myshkis A: Applied Theory of Functional Differential Equations. Kluwer Academic, Norwell; 1992.

Govindan TE: Exponential stability in mean-square of parabolic quasilinear stochasticdelay evolution equations. Stoch. Anal. Appl. 1999, 17: 443–461. 10.1080/07362999908809612

Ren Y, Chen L: A note on the neutral stochastic functional differential equations withinfinite delay and Poisson jumps in an abstract space. J. Math. Phys. 2009., 50: Article ID 082704

Ren Y, Lu S, Xia N: Remarks on the existence and uniqueness of the solutions to stochasticfunctional differential equations with infinite delay. J. Comput. Appl. Math. 2008, 220: 364–372. 10.1016/j.cam.2007.08.022

Ren Y, Xia N: Existence, uniqueness and stability of the solutions to neutral stochasticfunctional differential equations with infinite delay. Appl. Math. Comput. 2009, 210: 72–79. 10.1016/j.amc.2008.11.009

Ren Y, Xia N: A note on the existence and uniqueness of the solution to neutral stochasticfunctional differential equations with infinite delay. Appl. Math. Comput. 2009, 214: 457–461. 10.1016/j.amc.2009.04.013

Nieto JJ, Rodriguez-Lopez R: New comparison results for impulsive integro-differential equations andapplications. J. Math. Anal. Appl. 2007, 328: 1343–1368. 10.1016/j.jmaa.2006.06.029

Samoilenko AM, Perestyuk NA: Impulsive Differential Equations. World Scientific, Singapore; 1995.

Travis CC, Webb GF: Cosine families and abstract nonlinear second order differentialequations. Acta Math. Acad. Sci. Hung. 1978, 32: 76–96.

Fattorini HO North-Holland Mathematics Studies 108. In Second Order Linear Differential Equations in Banach Spaces. North-Holland, Amsterdam; 1985.

Travis CC, Webb GF: Second order differential equations in Banach space. In Proceedings of an International Symposium on Nonlinear Equations in AbstractSpaces. Academic Press, New York; 1987:331–361.

McKibben MA: Second-order damped functional stochastic evolution equations in Hilbertspace. Dyn. Syst. Appl. 2003, 12: 467–487.

Mahmudov NI, McKibben MA: Abstract second-order damped McKean-Vlasov stochastic evolution equations. Stoch. Anal. Appl. 2006, 24: 303–328. 10.1080/07362990500522247

McKibben MA: Second-order neutral stochastic evolution equations with heredity. J. Appl. Math. Stoch. Anal. 2004, 2004: 177–192. 10.1155/S1048953304309020

Balasubramaniam P, Muthukumar P: Approximate controllability of second-order stochastic distributed implicitfunctional differential systems with infinite delay. J. Optim. Theory Appl. 2009, 143: 225–244. 10.1007/s10957-009-9564-x

Da Prato G: Non-linear stochastic partial differential equations. In Mathematics of Complexity and Dynamical Systems. Springer, Berlin; 2011:1126–1136.

Li Y, Liu B: Existence of solution of nonlinear neutral functional differential inclusionswith infinite delay. Stoch. Anal. Appl. 2007, 25: 397–415. 10.1080/07362990601139610

Burton TA, Kirk C: A fixed point theorem of Krasnoselskii-Schaefer type. Math. Nachr. 1998, 189: 23–31. 10.1002/mana.19981890103