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Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay
1. | Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany |
2. | Institut für Stochastik, Friedrich Schiller Universität Jena, Ernst Abbe Platz 2, 07737 Jena, Germany |
References:
[1] |
Ludwig Arnold, "Random Dynamical Systems," Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998.
doi: 10.1007/BFb0095238. |
[2] |
Tomás Caraballo, Jinqiao Duan, Kening Lu and Björn Schmalfuß, Invariant manifolds for random and stochastic partial differential equations, Adv. Nonlinear Stud., 10 (2010), 23-52. |
[3] |
Tomás Caraballo, María J. Garrido-Atienza, Björn Schmalfuß and José Valero, Non-autonomous and random attractors for delay random semilinear equations without uniqueness, Discrete Contin. Dyn. Syst., 21 (2008), 415-443.
doi: 10.3934/dcds.2008.21.415. |
[4] |
Tomás Caraballo, Peter E. Kloeden and José Real, Discretization of asymptotically stable stationary solutions of delay differential equations with a random stationary delay, J. Dynam. Differential Equations, 18 (2006), 863-880.
doi: 10.1007/s10884-006-9022-5. |
[5] |
Carmen Chicone and Yuri Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs, 70, American Mathematical Society, Providence, RI, 1999. |
[6] |
Igor D. Chueshov, "Introduction to the Theory of Infinite-Dimensional Dissipative Systems," AKTA, Kharkiv, 2002. |
[7] |
Igor D. Chueshov and M. Scheutzow, Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations, J. Dynam. Differential Equations, 13 (2001), 355-380.
doi: 10.1023/A:1016684108862. |
[8] |
Thai S. Doan and Stefan Siegmund, Differential equations with random delay,, Infinite dimensional dynamical systems., ().
|
[9] |
María J. Garrido-Atienza, Kening Lu and Björn Schmalfuß, Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion, J. Differential Equations, 248 (2010), 1637-1667.
doi: 10.1016/j.jde.2009.11.006. |
[10] |
María J. Garrido-Atienza, Arne Ogrowsky and Björn Schmalfuß, Random differential equations with random delays, Stoch. Dyn., 11 (2011), 369-388.
doi: 10.1142/S0219493711003358. |
[11] |
Salah-Eldin A. Mohammed, Tusheng Zhang and Huaizhong Zhao, The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations, Mem. Amer. Math. Soc., 196 (2008), vi+105 pp. |
show all references
References:
[1] |
Ludwig Arnold, "Random Dynamical Systems," Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998.
doi: 10.1007/BFb0095238. |
[2] |
Tomás Caraballo, Jinqiao Duan, Kening Lu and Björn Schmalfuß, Invariant manifolds for random and stochastic partial differential equations, Adv. Nonlinear Stud., 10 (2010), 23-52. |
[3] |
Tomás Caraballo, María J. Garrido-Atienza, Björn Schmalfuß and José Valero, Non-autonomous and random attractors for delay random semilinear equations without uniqueness, Discrete Contin. Dyn. Syst., 21 (2008), 415-443.
doi: 10.3934/dcds.2008.21.415. |
[4] |
Tomás Caraballo, Peter E. Kloeden and José Real, Discretization of asymptotically stable stationary solutions of delay differential equations with a random stationary delay, J. Dynam. Differential Equations, 18 (2006), 863-880.
doi: 10.1007/s10884-006-9022-5. |
[5] |
Carmen Chicone and Yuri Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs, 70, American Mathematical Society, Providence, RI, 1999. |
[6] |
Igor D. Chueshov, "Introduction to the Theory of Infinite-Dimensional Dissipative Systems," AKTA, Kharkiv, 2002. |
[7] |
Igor D. Chueshov and M. Scheutzow, Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations, J. Dynam. Differential Equations, 13 (2001), 355-380.
doi: 10.1023/A:1016684108862. |
[8] |
Thai S. Doan and Stefan Siegmund, Differential equations with random delay,, Infinite dimensional dynamical systems., ().
|
[9] |
María J. Garrido-Atienza, Kening Lu and Björn Schmalfuß, Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion, J. Differential Equations, 248 (2010), 1637-1667.
doi: 10.1016/j.jde.2009.11.006. |
[10] |
María J. Garrido-Atienza, Arne Ogrowsky and Björn Schmalfuß, Random differential equations with random delays, Stoch. Dyn., 11 (2011), 369-388.
doi: 10.1142/S0219493711003358. |
[11] |
Salah-Eldin A. Mohammed, Tusheng Zhang and Huaizhong Zhao, The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations, Mem. Amer. Math. Soc., 196 (2008), vi+105 pp. |
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