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Volumn 2, Issue 4, 2005, Pages 919-962

ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION

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EID: 34547283966     PISSN: 02198916     EISSN: 17936993     Source Type: Journal    
DOI: 10.1142/S021989160500066X     Document Type: Article
Times cited : (15)

References (20)
  • 1
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations. I. Existence of a ground state
    • H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Ration. Mech. Anal. 82(4) (1983) 313–345.
    • (1983) Arch. Ration. Mech. Anal , vol.82 , Issue.4 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 2
    • 0000246714 scopus 로고    scopus 로고
    • Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
    • (1998)
    • J. Bourgain and W. Wang, Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25(1–2) (1997) 197–215 (1998).
    • (1997) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.25 , Issue.1–2 , pp. 197-215
    • Bourgain, J.1    Wang, W.2
  • 4
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
    • J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case, J. Funct. Anal. 32(1) (1979) 1–32.
    • (1979) J. Funct. Anal , vol.32 , Issue.1 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 6
    • 0000893351 scopus 로고
    • Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
    • M. J. Landman, G. C. Papanicolaou, C. Sulem and P.-L. Sulem, Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension, Phys. Rev. A (3) 38(8) (1988) 3837–3843.
    • (1988) Phys. Rev. A (3) , vol.38 , Issue.8 , pp. 3837-3843
    • Landman, M. J.1    Papanicolaou, G. C.2    Sulem, C.3    Sulem, P.-L.4
  • 7
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case. I
    • P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linaire 1(2) (1984) 109–145.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linaire , vol.1 , Issue.2 , pp. 109-145
    • Lions, P.-L.1
  • 8
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case. II
    • P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linaire 1(4) (1984) 223–283.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linaire , vol.1 , Issue.4 , pp. 223-283
    • Lions, P.-L.1
  • 9
    • 0001337201 scopus 로고
    • Construction of solutions with exact k blow up points for the Schrödinger equation with critical power
    • F. Merle, Construction of solutions with exact k blow up points for the Schrödinger equation with critical power, Commun. Math. Phys. 129 (1990) 223–240.
    • (1990) Commun. Math. Phys , vol.129 , pp. 223-240
    • Merle, F.1
  • 10
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
    • F. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J. 69(2) (1993) 427–454.
    • (1993) Duke Math. J , vol.69 , Issue.2 , pp. 427-454
    • Merle, F.1
  • 11
    • 20444437961 scopus 로고    scopus 로고
    • Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation
    • F. Merle and P. Raphael, Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation, Ann. Math. 161(1) (2005) 157–222.
    • (2005) Ann. Math , vol.161 , Issue.1 , pp. 157-222
    • Merle, F.1    Raphael, P.2
  • 12
    • 0041350485 scopus 로고    scopus 로고
    • Sharp upper bound on the blow up rate for critical nonlinear Schrödinger equation
    • F. Merle and P. Raphael, Sharp upper bound on the blow up rate for critical nonlinear Schrödinger equation, Geom. Funct. Anal. 13 (2003) 591–642.
    • (2003) Geom. Funct. Anal , vol.13 , pp. 591-642
    • Merle, F.1    Raphael, P.2
  • 13
    • 2942586742 scopus 로고    scopus 로고
    • 2 critical nonlinear Schrödinger equation
    • 2 critical nonlinear Schrödinger equation, Invent. Math. 156 (2004) 565–672.
    • (2004) Invent. Math , vol.156 , pp. 565-672
    • Merle, F.1    Raphael, P.2
  • 14
    • 85189426131 scopus 로고    scopus 로고
    • Sharp lower bound on the blow up rate for critical nonlinear Schrödinger equation
    • to appear in
    • F. Merle and P. Raphael, Sharp lower bound on the blow up rate for critical nonlinear Schrödinger equation, to appear in J. Amer. Math. Soc.
    • J. Amer. Math. Soc
    • Merle, F.1    Raphael, P.2
  • 15
    • 12444281836 scopus 로고    scopus 로고
    • Profiles and quantization of the blow up mass fro critical non-linear Schrödinger equation
    • F. Merle and P. Raphael, Profiles and quantization of the blow up mass fro critical non-linear Schrödinger equation, Commun. Math. Phys. 253 (2005) 675–704.
    • (2005) Commun. Math. Phys , vol.253 , pp. 675-704
    • Merle, F.1    Raphael, P.2
  • 16
    • 0000704928 scopus 로고
    • 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
    • 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power nonlinearity, J. Differential Equations 84 (1990) 205–214.
    • (1990) J. Differential Equations , vol.84 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 17
    • 0035537074 scopus 로고    scopus 로고
    • On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D
    • G. Perelman, On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D, Ann. Henri. Poincaré 2 (2001) 605–673.
    • (2001) Ann. Henri. Poincaré , vol.2 , pp. 605-673
    • Perelman, G.1
  • 18
    • 13844296411 scopus 로고    scopus 로고
    • Stability of the log-log bound for blow up solutions to the critical nonlinear Schrödinger equation
    • P. Raphael, Stability of the log-log bound for blow up solutions to the critical nonlinear Schrödinger equation, Math. Annal. 331 (2005) 577–609.
    • (2005) Math. Annal , vol.331 , pp. 577-609
    • Raphael, P.1
  • 20
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M. I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys. 87 (1983) 567–576.
    • (1983) Commun. Math. Phys , vol.87 , pp. 567-576
    • Weinstein, M. I.1


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