ATTRACTING AND QUASI-INVARIANT SETS OF STOCHASTIC NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(13)60021-1

Abstract

CLC Number:

35B35

LI Ding-Shi, XU Dao-Xi. ATTRACTING AND QUASI-INVARIANT SETS OF STOCHASTIC NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series B, 2013, 33(2): 578-588.

Trendmd

[1] Cheban D, Mammana C. Invariant manifolds, global attractors and almost periodic solutions of nonau-tonomous difference equations. Nonlinear Anal, 2004, 56: 465–484

[2] Xu D Y. Asymptotic behavior of nonlinear difference equations with delays. Comput Math Appl, 2001, 42: 393–398

[3] Xu D Y. Invariant and attracting sets of Volterra difference equations with delays. Comput Math Appl, 2003, 45: 1311–1317

[4] Bernfeld S R, Corduneanu C, Ignatyev A O. On the stability of invariant sets of functional differential equations. Nonlinear Anal, 2003, 55: 641–656

[5] Kolmanovskii V B, Nosov V R. Stability of Functional Differential Equations. Orlando, FL: Academic Press, 1986

[6] Liao X X, Luo Q, Zeng Z G. Positive invariant and global exponential attractive sets of neural networks with time-varying delays. Neurocomputing, 2008, 71: 513–518

[7] Xu D Y, Zhao H Y. Invariant set and attractivity of nonlinear differential equations with delays. Appl Math Lett, 2002, 15 : 321–325

[8] Zhao H Y. Invariant set and attractor of nonautonomous functional differential systems. J Math Anal Appl, 2003, 282: 437–443

[9] Wang L S, Xu D Y. Asymptotic behavior of a class of reaction-diffusion equations with delays. J Math Anal Appl, 2003, 281: 439–453

[10] Duan J Q, Lu K N, Schmalfuß B. Invariant manifolds for stochastic partial differential equations. Ann Probab, 2003, 31: 2109–2135

[11] Lu K N, Schmalfuß B. Invariant manifolds for stochastic wave equations. J Differential Equations, 2007, 236: 460–492

[12] Liu K, Xia X, On the exponential stability in mean square of neutral stochastic functional differential equations. Systems Control Lett, 1999, 37: 207–215

[13] Govindan T E. Almost sure exponential stability for stochastic neutral partial functional differential equa-tions. Stochastics, 2005, 77: 139–154

[14] Caraballo T, Real J, Taniguchi T. The exponential stability of neutral stochastic delay partial differential equations. Discrete Contin Dyn Syst, 2007, 18: 295–313

[15] Caraballo T, Liu K. Exponential stability of mild solutions of stochastic partial differential equations with delays. Stoch Anal Appl, 1999, 17: 743–763

[16] Luo J W. Exponential stability for stochastic neutral partial functional differential equations. J Math Anal Appl, 2009, 355: 414–425

[17] Luo J W. Fixed points and stability of neutral stochastic delay differential equations. J Math Anal Appl, 2007, 334: 431–440

[18] Chen H B. Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays. Statist Probab Lett, 2010, 80: 50–56

[19] Bao J H, Hou Z T. Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients. Comput Math Appl, 2010, 59: 207–214

[20] Chen H B. Integral inequality and exponential stability for neutral stochastic partial differential equations with delays. Journal of Inequalities and Applications, 2009: Article ID 297478

[21] Boufoussi B, Hajji S. Successive approximation of neutral functional stochastic differential equations with jumps. Statist Probal Lett, 2010, 80: 324–332

[22] Jiang F, Shen Y. A note on the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations with non-Lipschitz coefficients. Comput Math Appl, 2011, 61: 1590–1594

[23] Prato G Da, Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge Univ Press, 1992

[24] Pazy A. Semigroups of linear operators and applications to partial differential equations//Applied Methe-matical Sciences. Vol 44. New York: Springer Verlag, 1983

[25] Ichikawa A. Stability of semilinear stochastic evolution equations. J Math Anal Appl, 1982, 90: 12–44

[26] Wu F, Hu S, Liu Y. Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system. J Math Anal Appl, 2010, 364: 104–118

[27] Xu D Y, Huang Y M, Yang Z G. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete Contin Dyn Syst, 2009, 24: 1005–1023

ATTRACTING AND QUASI-INVARIANT SETS OF STOCHASTIC NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Jing FU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI. QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM [J]. Acta mathematica scientia,Series B, 2018, 38(2): 429-440.
[2]	Yuecai HAN, Yifang SUN. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS [J]. Acta mathematica scientia,Series B, 2018, 38(2): 681-694.
[3]	Zhiming WANG. EULER SCHEME AND MEASURABLE FLOWS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS [J]. Acta mathematica scientia,Series B, 2018, 38(1): 157-168.
[4]	Junfeng LIU, Ciprian A. TUDOR. STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY [J]. Acta mathematica scientia,Series B, 2017, 37(6): 1545-1566.
[5]	Van Hien LE, Dinh Ke TRAN, Trong Kinh CHU. GLOBALLY ATTRACTING SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS OF SOBOLEV TYPE [J]. Acta mathematica scientia,Series B, 2017, 37(5): 1295-1318.
[6]	Qun LIU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI. DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH [J]. Acta mathematica scientia,Series B, 2017, 37(4): 927-940.
[7]	Jing CUI, Litan YAN. CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION [J]. Acta mathematica scientia,Series B, 2017, 37(1): 108-118.
[8]	Heping MA, Biu LIU. EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY [J]. Acta mathematica scientia,Series B, 2017, 37(1): 235-258.
[9]	Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM. EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1509-1523.
[10]	Xianghua ZHANG, Fu CHEN, Ke WANG, Hong DU. STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE [J]. Acta mathematica scientia,Series B, 2016, 36(3): 740-752.
[11]	Wenqiang ZHAO. REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE [J]. Acta mathematica scientia,Series B, 2016, 36(2): 409-427.
[12]	Yue GUAN, Hua ZHANG. CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2016, 36(2): 487-498.
[13]	Xiaoli DING, Juan J. NIETO. CONTROLLABILITY AND OPTIMALITY OF LINEAR TIME-INVARIANT NEUTRAL CONTROL SYSTEMS WITH DIFFERENT FRACTIONAL ORDERS [J]. Acta mathematica scientia,Series B, 2015, 35(5): 1003-1013.
[14]	Qixia ZHANG, Qiliang SUN. A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H₂/H_∞ CONTROL WITH RANDOM JUMPS [J]. Acta mathematica scientia,Series B, 2015, 35(2): 348-358.
[15]	MA Qing-Xia, LIU An-Ping. OSCILLATION CRITERIA OF NEUTRAL TYPE IMPULSIVE HYPERBOLIC EQUATIONS [J]. Acta mathematica scientia,Series B, 2014, 34(6): 1845-1853.