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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 10
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Articles

Stability of standing waves for the L2-critical Hartree equations with harmonic potential

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Pages 2076-2083 | Received 03 May 2012, Accepted 24 Jul 2012, Published online: 29 Aug 2012

References

  • Frühlich , J and Lenzmann , E . 2004 . Mean-field limit of quantum Bose gases and nonlinear Hartree equation . Smin. Eqns Dériv. Partielles , XIX : 1 – 26 .
  • Lieb , EH , Seiringer , R , Solovej , JP and Yngvason , J . 2003 . “ The quantum-mechanical many-body problem: The Bose gas ” . In Perspectives in Analysis (KTH Stockholm) , Edited by: Benedicks , M , Jones , P and Smirnov , S . Berlin : Springer .
  • Berestycki , H and Cazenave , T . 1981 . Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéarires . C.R. Acad. Sci. Paris, Ser. I , 293 : 489 – 492 .
  • Bona , J and Chen , H . 2002 . Solitary waves in nonlinear dispersive systems . Discrete Contin. Dyn. Syst. Ser. B , 2 ( 3 ) : 313 – 378 .
  • Cazenave , T and Lions , PL . 1982 . Orbital stability of standing waves for some nonlinear Schrödinger equations . Commun. Math. Phys. , 85 ( 4 ) : 549 – 561 .
  • Chen , J and Guo , B . 2007 . Strong instability of standing waves for a nonlocal Schrödinger equation . Physica D , 227 : 142 – 148 .
  • Datchev , K and Ventura , I . 2009 . Solitary waves for the Hartree equation with a slowly varying potential (2009). Available at: arXiv0904.0834vl
  • Fukuizumi , R . 2001 . Stability and instability of standing waves for the nonlinear Schrödinger equation with Harmonic potential . Discrete Contin. Dyn. Syst. , 7 : 525 – 544 .
  • Fukuizumi , R and Ohta , M . 2003 . Stability of standing waves for nonlinear Schrodinger equations with potentials . Differ. Integral Eqns , 16 : 111 – 128 .
  • Fukuizumi , R and Ohta , M . 2003 . Instability of standing waves for nonlinear Schrödinger equations with potentials . Differ. Integral Eqns , 16 : 691 – 706 .
  • Wang , Y . 2008 . Strong instability of standing waves for Hartree equation with harmonic potential . Physica D , 237 : 998 – 1005 .
  • Zhang , J . 2000 . Stability of atrractive Bose-Einstein condensates . J. Stat. Phys. , 101 ( 3/4 ) : 731 – 746 .
  • Cazenave , T . 2003 . “ Semilinear Schrödinger Equations ” . In Courant Lecture Notes in Mathematics , Vol. 10 , New York : New York University Courant Institute of Mathematical Sciences .
  • Weinstein , MI . 1983 . Nonlinear Schrödinger equations and sharp interpolations estimates . Commun. Math. Phys. , 87 : 567 – 576 .
  • Zhang , J . 2005 . Sharp threshold for blowup and global existence in nonlinear Schrodinger equations under a harmonic potential . Commun. Partial Differ. Eqns , 30 : 1429 – 1443 .
  • Oh , Y . 1991 . Cauchy problem and Ehrenfest's law of nonlinear Schrödinger equations with potentials . J. Differ. Eqns , 92 : 255 – 274 .
  • Miao , C , Xu , G and Zhao , L . 2010 . On the blow up phenomenon for the L 2-critical focusing Hartree equation . Colloquium Math. , 119 : 23 – 50 .

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