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Journal of Difference Equations and Applications Volume 17, 2011 - Issue 2: Non-autonomous difference equations and discrete dynamical systems
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Original Articles

Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity

T. Caraballo Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, SpainCorrespondence[email protected]
,
F. Morillas Departament d'Economia Aplicada, Facultat d'Economia, Universitat de València, Campus dels Tarongers s/n, 46022, València, Spain
&
J. Valero Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. Universidad s/n, 03202, Elche, Alicante, Spain
Pages 161-184 | Received 07 Jul 2009, Published online: 18 Mar 2011

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Fengling Wang & Yangrong Li. (2021) Random attractors for multi-valued multi-stochastic delayed p-Laplace lattice equations. Journal of Difference Equations and Applications 27:8, pages 1232-1258.
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Shuang Yang & Yangrong Li. (2020) Asymptotic autonomous attractors for a stochastic lattice model with random viscosity. Journal of Difference Equations and Applications 26:4, pages 540-560.
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Articles from other publishers (32)

Xiaolan Qin, Lianbing She & Renhai Wang. (2023) Mean random attractors of stochastic lattice fractional delay Gray–Scott equations in higher moment product sequence spaces. Banach Journal of Mathematical Analysis 17:4.
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Ahmed Y. Abdallah. (2023) Random Uniform Attractors for First Order Stochastic Non-Autonomous Lattice Systems. Qualitative Theory of Dynamical Systems 22:2.
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Pengyu Chen, Bixiang Wang, Renhai Wang & Xuping Zhang. (2022) Multivalued random dynamics of Benjamin-Bona-Mahony equations driven by nonlinear colored noise on unbounded domains. Mathematische Annalen 386:1-2, pages 343-373.
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Wenqiang Zhao & Zhi Li. (2023) CONTINUITY OF SOLUTIONS IN <inline-formula><tex-math id="M1">$ H^1( {\mathbb{R}}^N)\cap L^{p}( {\mathbb{R}}^N) $</tex-math></inline-formula> FOR STOCHASTIC REACTION-DIFFUSION EQUATIONS AND ITS APPLICATIONS TO PULLBACK ATTRACTOR. Journal of Applied Analysis & Computation 13:6, pages 3308-3329.
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Lei Na & Zhou Shengfan. (2021) Upper semicontinuity of uniform attractors fornon-autonomous lattice systems under singular perturbations. SCIENTIA SINICA Mathematica 52:10, pages 1121.
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M. J. Garrido-Atienza, B. Schmalfuß & J. Valero. (2022) Random attractors for setvalued dynamical systems for stochastic evolution equations driven by a nontrivial fractional noise. Stochastics and Dynamics 22:03.
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Panpan Zhang & Anhui Gu. (2021) Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms. Stochastics and Dynamics 22:02.
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Xiaoying Han & Peter E. Kloeden. (2022) Pullback and forward dynamics of nonautonomous Laplacian lattice systems on weighted spaces. Discrete and Continuous Dynamical Systems - S 15:10, pages 2909.
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Yusen Lin & Dingshi Li. (2022) Limiting behavior of invariant measures of highly nonlinear stochastic retarded lattice systems. Discrete and Continuous Dynamical Systems - B 27:12, pages 7561.
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Ahmed Y. Abdallah, Taqwa M. Al-Khader & Heba N. Abu-Shaab. (2022) Attractors of the Klein-Gordon-Schrödinger lattice systems with almost periodic nonlinear part. Discrete and Continuous Dynamical Systems - B 27:11, pages 6481.
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Jingyu Wang, Yejuan Wang & Tomás Caraballo. (2022) Multi-valued random dynamics of stochastic wave equations with infinite delays. Discrete and Continuous Dynamical Systems - B 27:10, pages 6147.
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Ahmed Y. Abdallah. (2021) Dynamics of Second Order Lattice Systems with Almost Periodic Nonlinear Part. Qualitative Theory of Dynamical Systems 20:2.
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Xiaoli Wang, Peter E. Kloeden & Xiaoying Han. (2021) Stochastic dynamics of a neural field lattice model with state dependent nonlinear noise. Nonlinear Differential Equations and Applications NoDEA 28:4.
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Rania T. Wannan & Ahmed Y. Abdallah. (2020) Long-Time Behavior of Non-Autonomous FitzHugh–Nagumo Lattice Systems. Qualitative Theory of Dynamical Systems 19:3.
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Wenqiang Zhao, Yijin Zhang & Shangjie Chen. (2020) Higher-order Wong–Zakai approximations of stochastic reaction–diffusion equations on . Physica D: Nonlinear Phenomena 401, pages 132147.
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Xiaoying Han & Peter E. Kloeden. 2019. Modeling, Stochastic Control, Optimization, and Applications. Modeling, Stochastic Control, Optimization, and Applications 201 233 .
Bixiang Wang. (2017) Multivalued non-autonomous random dynamical systems for wave equations without uniqueness. Discrete & Continuous Dynamical Systems - B 22:5, pages 2011-2051.
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Chengjian Zhang & Lu Zhao. (2017) The attractors for 2nd-order stochastic delay lattice systems. Discrete & Continuous Dynamical Systems - A 37:1, pages 575-590.
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Jingyu Wang, Yejuan Wang & Dun Zhao. (2016) Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays. Stochastics and Dynamics 16:05, pages 1750001.
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Ahmed Y. Abdallah. (2016) Attractors for second order lattice systems with almost periodic symbols in weighted spaces. Journal of Mathematical Analysis and Applications 442:2, pages 761-781.
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Yejuan Wang, Jiaohui Xu & Peter E. Kloeden. (2016) Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative. Nonlinear Analysis: Theory, Methods & Applications 135, pages 205-222.
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Tomás Caraballo, Xiaoying Han, Björn Schmalfuss & José Valero. (2016) Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise. Nonlinear Analysis 130, pages 255-278.
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Yejuan Wang & Jingyu Wang. (2015) Pullback attractors for multi-valued non-compact random dynamical systems generated by reaction–diffusion equations on an unbounded domain. Journal of Differential Equations 259:2, pages 728-776.
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Tomás Caraballo, Francisco Morillas & José Valero. (2015) Attractors for non-autonomous retarded lattice dynamical systems. Nonautonomous Dynamical Systems 2:1.
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Tomás Caraballo & Xiaoying Han. (2015) A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions. Discrete & Continuous Dynamical Systems - S 8:6, pages 1079-1101.
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Xiaoying Han. 2015. Continuous and Distributed Systems II. Continuous and Distributed Systems II 121 136 .
Tomás Caraballo, Francisco Morillas & José Valero. (2014) Asymptotic behaviour of a logistic lattice system. Discrete and Continuous Dynamical Systems 34:10, pages 4019-4037.
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Tomás Caraballo, Francisco Morillas & José Valero. (2014) On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems - A 34:1, pages 51-77.
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Xiaolin Jia, Caidi Zhao & Juan Cao. (2014) Uniform attractor of the non-autonomous discrete Selkov model. Discrete & Continuous Dynamical Systems - A 34:1, pages 229-248.
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Tomás Caraballo, Francisco Morillas & José Valero. 2013. Differential and Difference Equations with Applications. Differential and Difference Equations with Applications 341 349 .
Tomás Caraballo, F. Morillas & J. Valero. (2012) Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities. Journal of Differential Equations 253:2, pages 667-693.
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Xiaoquan Ding & Jifa Jiang. (2012) Random Attractors for Stochastic Retarded Lattice Dynamical Systems. Abstract and Applied Analysis 2012, pages 1-27.
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