Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity

References

• Abdallah , A.Y. 2008 . Exponential attractors for first-order lattice dynamical systems . J. Math. Anal. Appl. , 339 : 217 – 224 .
   Web of Science ®Google Scholar
• Arnold , L. 1998 . Random Dynamical Systems , Berlin : Springer-Verlag .
   Google Scholar
• Bates , P.W. , Lu , K. and Wang , B. 2001 . Attractors for lattice dynamical systems . Int. J. Bifur. Chaos , 11 : 143 – 153 .
   Web of Science ®Google Scholar
• Bates , P.W. , Lisei , H. and Lu , K. 2006 . Attractors for stochastic lattice dynamical systems . Stoch. Dyn. , 6 : 1 – 21 .
   Web of Science ®Google Scholar
• Beyn , W.J. and Pilyugin , S.Y. 2003 . Attractors of reaction diffusion systems on infinite lattices . J. Dynam. Differ. Equ. , 15 : 485 – 515 .
   Google Scholar
• Caraballo , T. and Lu , K. 2008 . Attractors for stochastic lattice dynamical systems with a multiplicative noise . Front. Math. China , 3 : 317 – 335 .
   Web of Science ®Google Scholar
• Caraballo , T. , Langa , J.A. and Valero , J. 2001 . Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise . J. Math. Anal. Appl. , 260 : 602 – 622 .
   Web of Science ®Google Scholar
• Caraballo , T. , Langa , J.A. and Valero , J. 2002 . Global attractors for multivalued random dynamical systems . Nonlinear Anal. , 48 : 805 – 829 .
   Web of Science ®Google Scholar
• Caraballo , T. , Kloeden , P.E. and Schmalfuß , B. 2004 . Exponentially stable stationary solutions for stochastic evolution equations and their perturbation . Appl. Math. Optim. , 50 : 183 – 207 .
   Web of Science ®Google Scholar
• Caraballo , T. , Garrido-Atienza , M.J. , Schmalfuß , B. and Valero , J. 2008 . Non-autonomous and random attractors for delay random semilinear equations without uniqueness . Discrete Contin. Dyn. Syst. , 21 : 415 – 443 .
   Web of Science ®Google Scholar
• T. Caraballo, M.J. Garrido-Atienza, B. Schmalfuß, and J. Valero, Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions, Discrete Contin. Dyn. Syst. Ser. B 14 (2010), pp. 439–455
   Google Scholar
• Castaing , C. and Valadier , M. 1977 . Convex Analysis and Measurable Multifunctions , Lecture Notes in Mathematics Vol. 580 , Berlin : Springer-Verlag .
   Google Scholar
• Hu , S. and Papageorgiou , N.S. 1997 . Handbook of Multivalued Analysis. Volume 1: Theory , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Karachalios , N.I. and Yannacopoulos , A.N. 2005 . Global existence and compact attractors for the discrete nonlinear Schrödinger equations . J. Differ. Equ. , 217 : 88 – 123 .
   Web of Science ®Google Scholar
• Karachalios , N.I. , Nistazakis , H.E. and Yannacopoulos , A.N. 2007 . Asymptotic behavior of solutions of complex discrete evolution equations: The discrete Ginzburg-Landau equation . Discrete Contin. Dyn. Syst. , 19 : 711 – 736 .
   Web of Science ®Google Scholar
• Kato , S. 1976 . On existence and uniqueness conditions for nonlinear ordinary differential equations in Banach spaces . Funkcialaj Ekvacioj. , 19 : 239 – 245 .
   Google Scholar
• Morillas , F. and Valero , J. 2009 . A Peano's theorem and attractors for lattice dynamical systems . Int. J. Bifur. Chaos , 19
   Google Scholar
• Oliveira , J.C. , Pereira , J.M. and Perla Menzala , G. 2008 . Attractors for second order periodic lattices with nonlinear damping . J. Differ. Equ. Appl. , 14 ( 9 ) : 899 – 921 .
   Web of Science ®Google Scholar
• Schmalfuß , B. 2000 . “ Attractors for the non-autonomous dynamical systems ” . In International Conference on Differential Equations, Vols. 1, 2 (Berlin, 1999) , 684 – 689 . River Edge, NY : World Scientific Publishing .
   Google Scholar
• Wang , B. 2007 . Asymptotic behavior of non-autonomous lattice systems . J. Math. Anal. Appl. , 331 : 121 – 136 .
   Web of Science ®Google Scholar
• Wang , Y. , Liu , Y. and Wang , Z. 2008 . Random attractors for partly dissipative stochastic lattice dynamical systems . J. Differ. Equ. Appl. , 14 ( 8 ) : 799 – 817 .
   Web of Science ®Google Scholar
• Zhao , C. and Zhou , S. 2007 . Attractor of retarded first order lattice systems . Nonlinearity , 20 : 1987 – 2006 .
   Web of Science ®Google Scholar
• Zhou , S. 2004 . Attractors and approximations for lattice dynamical systems . J. Differ. Equ. , 200 : 342 – 368 .
   Web of Science ®Google Scholar
• Zhou , S. and Shi , W. 2006 . Attractors and dimension of dissipative lattice systems . J. Differ. Equ. , 224 : 172 – 204 .
   Web of Science ®Google Scholar