Skip to main content
SpringerLink
Log in

Attractors for discrete nonlinear Schrödinger equation with delay

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, we first prove the existence of the global attractor A v ε C([−v,0],ℓ2) (v>0) for a weak damping discrete nonlinear Schrödinger equation with delay. Then we consider an upper semi-continuity of A v as v → 0+.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Caraballo T., Real, J. Attractors for 2D-Navier-Stokes models with delays. J. Diff. Eqns, 205: 271–297 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chepyzhov, V.V., Vishik, M.I. Attractors for equations of mathematical physics. AMS Colloquium Publications, 49. AMS, Providence, RI., 2002

    MATH  Google Scholar 

  3. Hale, J.K. Theorey of functional differential equations. Springer-Verlag, New York, 1977

    Google Scholar 

  4. Hines G. Upper semicontinuity of the attractor with respect to parameter dependent delays. J. Diff. Eqns.. 123: 56–92 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Karachalios, N., Yannacopoulos, A. Global existence and compact attractros for the discrete nonlinear Schrödinger equation. J. Diff. Eqns., 217: 88–123 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Temam, R. Infinite-dimensional dynamical systems in mechaics and physics. Appl. Math. Sci., 68, Springer-Verlag, Berlin, 2nd ed., 1997

    Google Scholar 

  7. Wu, J. Theory and applications of partial functional-diffrential equations. Applied Mathematical Sciences, 119, Springer-Verlag, New York, 1996

    Google Scholar 

  8. Zhao, C., Zhou, S. Attractors for retarded first order lattice systems. Nonlinearity, 20: 1987–2006 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Admissions and Career Service, Shanghai University, Shanghai, 200444, China

    Tao Chen

  2. Department of Applied Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Sheng-fan Zhou

  3. Department of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, China

    Cai-di Zhao

Authors
  1. Tao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-fan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cai-di Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sheng-fan Zhou.

Additional information

Supported by the National Natural Science Foundation of China (No. 10771139, 10826091), the Natural Science Foundation of Wenzhou University with item (No. 2007L024) and the Innovation Program of Shanghai Municipal Education Commission (No. 08ZZ70) and Leading Academic Discipline Project of Shanghai Normal University (No.DZL707) and Foundation of Shanghai Normal University (No. DYL200803, PL715) and Natural Science Foundation of Zhejiang Province (No. Y6080077).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, T., Zhou, Sf. & Zhao, Cd. Attractors for discrete nonlinear Schrödinger equation with delay. Acta Math. Appl. Sin. Engl. Ser. 26, 633–642 (2010). https://doi.org/10.1007/s10255-007-7101-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-007-7101-y

Keywords

2000 MR Subject Classification

Search

Navigation