-
1
-
-
0020591567
-
Nonlinear scalar field equations. I. Existence of a ground state
-
MR 84h:35054a
-
H. Berestycki and P.-L. Lions, "Nonlinear scalar field equations. I. Existence of a ground state", Arch. Rational Mech. Anal. 82:4 (1983), 313-345. MR 84h:35054a
-
(1983)
Arch. Rational Mech. Anal.
, vol.82
, Issue.4
, pp. 313-345
-
-
Berestycki, H.1
Lions, P.-L.2
-
2
-
-
84977279911
-
Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics 10
-
CIMS, New York, MR 2004j:35266 Zbl 1055.35003
-
T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics 10, CIMS, New York, 2003. MR 2004j:35266 Zbl 1055.35003
-
(2003)
, vol.10
-
-
Cazenave, T.1
-
3
-
-
0015249887
-
3=0 and a variational characterization of other solutions
-
MR 48 #11814 Zbl 0249.35029
-
3=0 and a variational characterization of other solutions", Arch. Rational Mech. Anal. 46 (1972), 81-95. MR 48 #11814 Zbl 0249.35029
-
(1972)
Arch. Rational Mech. Anal.
, vol.46
, pp. 81-95
-
-
Coffman, C.V.1
-
4
-
-
63949086654
-
Dynamic of threshold solutions for energy-critical NLS
-
MR 2010e:35258 Zbl 05603849
-
T. Duyckaerts and F. Merle, "Dynamic of threshold solutions for energy-critical NLS", Geom. Funct. Anal. 18:6 (2009), 1787-1840. MR 2010e:35258 Zbl 05603849
-
(2009)
Geom. Funct. Anal.
, vol.18
, Issue.6
, pp. 1787-1840
-
-
Duyckaerts, T.1
Merle, F.2
-
5
-
-
77951143619
-
Threshold solutions for the focusing 3D cubic Schrödinger equation
-
MR 2011c:35533 Zbl 1195.35276
-
T. Duyckaerts and S. Roudenko, "Threshold solutions for the focusing 3D cubic Schrödinger equation", Rev. Mat. Iberoam. 26:1 (2010), 1-56. MR 2011c:35533 Zbl 1195.35276
-
(2010)
Rev. Mat. Iberoam.
, vol.26
, Issue.1
, pp. 1-56
-
-
Duyckaerts, T.1
Roudenko, S.2
-
6
-
-
59349111935
-
Scattering for the non-radial 3D cubic nonlinear Schrödinger equation
-
MR 2010e:35257
-
T. Duyckaerts, J. Holmer, and S. Roudenko, "Scattering for the non-radial 3D cubic nonlinear Schrödinger equation", Math. Res. Lett. 15:6 (2008), 1233-1250. MR 2010e:35257
-
(2008)
Math. Res. Lett.
, vol.15
, Issue.6
, pp. 1233-1250
-
-
Duyckaerts, T.1
Holmer, J.2
Roudenko, S.3
-
7
-
-
33746745308
-
Proof of a spectral property related to the singularity formation for the L2 critical nonlinear Schrödinger equation
-
MR 2007d:35254 Zbl 1100.35097
-
G. Fibich, F. Merle, and P. Raphaël, "Proof of a spectral property related to the singularity formation for the L2 critical nonlinear Schrödinger equation", Phys. D 220:1 (2006), 1-13. MR 2007d:35254 Zbl 1100.35097
-
(2006)
Phys. D
, vol.220
, Issue.1
, pp. 1-13
-
-
Fibich, G.1
Merle, F.2
Raphaël, P.3
-
8
-
-
34249993538
-
Singular ring solutions of critical and supercritical nonlinear Schrödinger equations
-
MR 2008k:35440 Zbl 1118.35043
-
G. Fibich, N. Gavish, and X.-P. Wang, "Singular ring solutions of critical and supercritical nonlinear Schrödinger equations", Phys. D 231:1 (2007), 55-86. MR 2008k:35440 Zbl 1118.35043
-
(2007)
Phys. D
, vol.231
, Issue.1
, pp. 55-86
-
-
Fibich, G.1
Gavish, N.2
Wang, X.-P.3
-
9
-
-
77955700830
-
On blow-up solutions to the 3D cubic nonlinear Schrödinger equation
-
ID abm004. MR 2008i:35227
-
J. Holmer and S. Roudenko, "On blow-up solutions to the 3D cubic nonlinear Schrödinger equation", Appl. Math. Res. Express. AMRX 2007:1 (2007), Art. ID abm004. MR 2008i:35227
-
(2007)
Appl. Math. Res. Express. AMRX
, vol.2007
, Issue.1
-
-
Holmer, J.1
Roudenko, S.2
-
10
-
-
47749109045
-
A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
-
MR 2009h:35403 Zbl 1155.35094
-
J. Holmer and S. Roudenko, "A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation", Comm. Math. Phys. 282:2 (2008), 435-467. MR 2009h:35403 Zbl 1155.35094
-
(2008)
Comm. Math. Phys.
, vol.282
, Issue.2
, pp. 435-467
-
-
Holmer, J.1
Roudenko, S.2
-
11
-
-
77950937063
-
Divergence of infinite-variance nonradial solutions to the 3D NLS equation
-
MR 2011m:35353 Zbl 1195.35277
-
J. Holmer and S. Roudenko, "Divergence of infinite-variance nonradial solutions to the 3D NLS equation", Comm. Partial Differential Equations 35:5 (2010), 878-905. MR 2011m:35353 Zbl 1195.35277
-
(2010)
Comm. Partial Differential Equations
, vol.35
, Issue.5
, pp. 878-905
-
-
Holmer, J.1
Roudenko, S.2
-
12
-
-
79952911434
-
A class of solutions to the 3D cubic nonlinear Schrödinger equation that blows up on a circle
-
MR 2012b:35323 Zbl 1220.35159
-
J. Holmer and S. Roudenko, "A class of solutions to the 3D cubic nonlinear Schrödinger equation that blows up on a circle", Appl. Math. Res. Express. AMRX 2011:1 (2011), 23-94. MR 2012b:35323 Zbl 1220.35159
-
(2011)
Appl. Math. Res. Express. AMRX
, vol.2011
, Issue.1
, pp. 23-94
-
-
Holmer, J.1
Roudenko, S.2
-
13
-
-
77949739721
-
Blow-up criteria for the 3D cubic nonlinear Schrödinger equation
-
MR 2011c:35538 Zbl 1202.37105
-
J. Holmer, R. Platte, and S. Roudenko, "Blow-up criteria for the 3D cubic nonlinear Schrödinger equation", Nonlinearity 23:4 (2010), 977-1030. MR 2011c:35538 Zbl 1202.37105
-
(2010)
Nonlinearity
, vol.23
, Issue.4
, pp. 977-1030
-
-
Holmer, J.1
Platte, R.2
Roudenko, S.3
-
14
-
-
33750526878
-
Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case
-
MR 2007g:35232
-
C. E. Kenig and F. Merle, "Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case", Invent. Math. 166:3 (2006), 645-675. MR 2007g:35232
-
(2006)
Invent. Math.
, vol.166
, Issue.3
, pp. 645-675
-
-
Kenig, C.E.1
Merle, F.2
-
15
-
-
74549167807
-
The cubic nonlinear Schrödinger equation in two dimensions with radial data
-
MR 2010m:35487 Zbl 1187.35237
-
R. Killip, T. Tao, and M. Visan, "The cubic nonlinear Schrödinger equation in two dimensions with radial data", J. Eur. Math. Soc. .JEMS/ 11:6 (2009), 1203-1258. MR 2010m:35487 Zbl 1187.35237
-
(2009)
J. Eur. Math. Soc. .JEMS/
, vol.11
, Issue.6
, pp. 1203-1258
-
-
Killip, R.1
Tao, T.2
Visan, M.3
-
16
-
-
34249974409
-
Uniqueness of positive solutions of δu-uCup D0 in Rn
-
MR 90d:35015 Zbl 0676.35032
-
M. K. Kwong, "Uniqueness of positive solutions of δu-uCup D0 in Rn", Arch. Rational Mech. Anal. 105:3 (1989), 243-266. MR 90d:35015 Zbl 0676.35032
-
(1989)
Arch. Rational Mech. Anal.
, vol.105
, Issue.3
, pp. 243-266
-
-
Kwong, M.K.1
-
17
-
-
0000893351
-
Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
-
MR 89k:35218
-
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. MR 89k:35218
-
(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
-
18
-
-
0000296501
-
Symétrie et compacité dans les espaces de Sobolev
-
MR 84k:46027 Zbl 0501.46032
-
P.-L. Lions, "Symétrie et compacité dans les espaces de Sobolev", J. Funct. Anal. 49:3 (1982), 315-334. MR 84k:46027 Zbl 0501.46032
-
(1982)
J. Funct. Anal.
, vol.49
, Issue.3
, pp. 315-334
-
-
Lions, P.-L.1
-
19
-
-
0036922015
-
Existence of nonstationary bubbles in higher dimensions
-
MR 2004e:35213 Zbl 1040.35116
-
M. Mari̧s, "Existence of nonstationary bubbles in higher dimensions", J. Math. Pures Appl. .9/ 81:12 (2002), 1207-1239. MR 2004e:35213 Zbl 1040.35116
-
(2002)
J. Math. Pures Appl. .9/
, vol.81
, Issue.12
, pp. 1207-1239
-
-
Mari̧s, M.1
-
20
-
-
0035635809
-
Instability of solitons for the critical generalized Korteweg-de Vries equation
-
MR 2002g:35182 Zbl 0985.35071
-
Y. Martel and F. Merle, "Instability of solitons for the critical generalized Korteweg-de Vries equation", Geom. Funct. Anal. 11:1 (2001), 74-123. MR 2002g:35182 Zbl 0985.35071
-
(2001)
Geom. Funct. Anal.
, vol.11
, Issue.1
, pp. 74-123
-
-
Martel, Y.1
Merle, F.2
-
21
-
-
0000041774
-
Uniqueness of positive radial solutions of δuCf .u/ D 0 in Rn. II
-
MR 94b:35105 Zbl 0804.35034
-
K. McLeod, "Uniqueness of positive radial solutions of δuCf .u/ D 0 in Rn. II", Trans. Amer. Math. Soc. 339:2 (1993), 495-505. MR 94b:35105 Zbl 0804.35034
-
(1993)
Trans. Amer. Math. Soc.
, vol.339
, Issue.2
, pp. 495-505
-
-
McLeod, K.1
-
22
-
-
84974001368
-
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
-
MR 94b:35262 Zbl 0808.35141
-
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. MR 94b:35262 Zbl 0808.35141
-
(1993)
Duke Math. J.
, vol.69
, Issue.2
, pp. 427-454
-
-
Merle, F.1
-
23
-
-
0041350485
-
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
-
MR 2005j:35207 Zbl 1061.35135
-
F. Merle and P. Raphael, "Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation", Geom. Funct. Anal. 13:3 (2003), 591-642. MR 2005j:35207 Zbl 1061.35135
-
(2003)
Geom. Funct. Anal.
, vol.13
, Issue.3
, pp. 591-642
-
-
Merle, F.1
Raphael, P.2
-
24
-
-
2942586742
-
On universality of blow-up profile for L2 critical nonlinear Schrödinger equation
-
MR 2006a:35283 Zbl 1067.35110
-
F. Merle and P. Raphael, "On universality of blow-up profile for L2 critical nonlinear Schrödinger equation", Invent. Math. 156:3 (2004), 565-672. MR 2006a:35283 Zbl 1067.35110
-
(2004)
Invent. Math.
, vol.156
, Issue.3
, pp. 565-672
-
-
Merle, F.1
Raphael, P.2
-
25
-
-
20444437961
-
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
-
MR 2006k:35277 Zbl 1185.35263
-
F. Merle and P. Raphael, "The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation", Ann. of Math. .2/ 161:1 (2005), 157-222. MR 2006k:35277 Zbl 1185.35263
-
(2005)
Ann. of Math. .2/
, vol.161
, Issue.1
, pp. 157-222
-
-
Merle, F.1
Raphael, P.2
-
26
-
-
12444281836
-
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
-
MR 2006m:35346 Zbl 1062.35137
-
F. Merle and P. Raphael, "Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation", Comm. Math. Phys. 253:3 (2005), 675-704. MR 2006m:35346 Zbl 1062.35137
-
(2005)
Comm. Math. Phys.
, vol.253
, Issue.3
, pp. 675-704
-
-
Merle, F.1
Raphael, P.2
-
27
-
-
30644464564
-
On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schrödinger equation
-
MR 2006j:35223 Zbl 1075.35077
-
F. Merle and P. Raphael, "On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schrödinger equation", J. Amer. Math. Soc. 19:1 (2006), 37-90. MR 2006j:35223 Zbl 1075.35077
-
(2006)
J. Amer. Math. Soc.
, vol.19
, Issue.1
, pp. 37-90
-
-
Merle, F.1
Raphael, P.2
-
28
-
-
80051968524
-
Global dynamics above the ground state energy for the cubic NLS equation in 3D
-
preprint, arXiv 1007.4025
-
K. Nakanishi and W. Schlag, "Global dynamics above the ground state energy for the cubic NLS equation in 3D", preprint, 2010. arXiv 1007.4025
-
(2010)
-
-
Nakanishi, K.1
Schlag, W.2
-
29
-
-
0000835523
-
Blow-up of H1 solution for the nonlinear Schrödinger equation
-
MR 92k:35262 Zbl 0739.35093
-
T. Ogawa and Y. Tsutsumi, "Blow-up of H1 solution for the nonlinear Schrödinger equation", J. Differential Equations 92:2 (1991), 317-330. MR 92k:35262 Zbl 0739.35093
-
(1991)
J. Differential Equations
, vol.92
, Issue.2
, pp. 317-330
-
-
Ogawa, T.1
Tsutsumi, Y.2
-
30
-
-
0035537074
-
On the formation of singularities in solutions of the critical nonlinear Schrödinger equation
-
MR 2002m:35205 Zbl 1007.35087
-
G. Perelman, "On the formation of singularities in solutions of the critical nonlinear Schrödinger equation", Ann. Henri Poincaré 2:4 (2001), 605-673. MR 2002m:35205 Zbl 1007.35087
-
(2001)
Ann. Henri Poincaré
, vol.2
, Issue.4
, pp. 605-673
-
-
Perelman, G.1
-
31
-
-
0000452161
-
Compact linear mappings between interpolation spaces
-
MR 29 #3871 Zbl 0128.35204
-
A. Persson, "Compact linear mappings between interpolation spaces", Ark. Mat. 5 (1964), 215-219. MR 29 #3871 Zbl 0128.35204
-
(1964)
Ark. Mat.
, vol.5
, pp. 215-219
-
-
Persson, A.1
-
32
-
-
13844296411
-
Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation
-
MR 2006b:35303
-
P. Raphael, "Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation", Math. Ann. 331:3 (2005), 577-609. MR 2006b:35303
-
(2005)
Math. Ann.
, vol.331
, Issue.3
, pp. 577-609
-
-
Raphael, P.1
-
33
-
-
33748575882
-
Existence and stability of a solution blowing up on a sphere for an L2-supercritical nonlinear Schrödinger equation
-
MR 2007k:35472 Zbl 1117.35077
-
P. Raphaël, "Existence and stability of a solution blowing up on a sphere for an L2-supercritical nonlinear Schrödinger equation", Duke Math. J. 134:2 (2006), 199-258. MR 2007k:35472 Zbl 1117.35077
-
(2006)
Duke Math. J.
, vol.134
, Issue.2
, pp. 199-258
-
-
Raphaël, P.1
-
34
-
-
70350025320
-
Standing ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation
-
MR 2010k:35469 Zbl 1184.35295
-
P. Raphaël and J. Szeftel, "Standing ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation", Comm. Math. Phys. 290:3 (2009), 973-996. MR 2010k:35469 Zbl 1184.35295
-
(2009)
Comm. Math. Phys.
, vol.290
, Issue.3
, pp. 973-996
-
-
Raphaël, P.1
Szeftel, J.2
-
35
-
-
0003230098
-
The nonlinear Schrödinger equation: self-focusing and wave collapse
-
Springer, New York,MR 2000f:35139 Zbl 0928.35157
-
C. Sulem and P.-L. Sulem, The nonlinear Schrödinger equation: self-focusing and wave collapse, Applied Mathematical Sciences 139, Springer, New York, 1999. MR 2000f:35139 Zbl 0928.35157
-
(1999)
Applied Mathematical Sciences
, vol.139
-
-
Sulem, C.1
Sulem, P.-L.2
-
36
-
-
69749083744
-
Nonlinear dispersive equations, CBMS Regional Conference Series in Mathematics: local and global analysis 106
-
Providence, RI, MR 2008i:35211 Zbl 1106.35001
-
T. Tao, Nonlinear dispersive equations, CBMS Regional Conference Series in Mathematics: local and global analysis 106, Amer. Math. Soc., Providence, RI, 2006. MR 2008i:35211 Zbl 1106.35001
-
(2006)
Amer. Math. Soc.
-
-
Tao, T.1
-
37
-
-
0041473959
-
Nonlinear Schrödinger equations and sharp interpolation estimates
-
MR 84d:35140 Zbl 0527.35023
-
M. I. Weinstein, "Nonlinear Schrödinger equations and sharp interpolation estimates", Comm. Math. Phys. 87:4 (1983), 567-576. MR 84d:35140 Zbl 0527.35023
-
(1983)
Comm. Math. Phys.
, vol.87
, Issue.4
, pp. 567-576
-
-
Weinstein, M.I.1
-
38
-
-
0000686130
-
Modulational stability of ground states of nonlinear Schrödinger equations
-
MR 86i:35130 Zbl 0583.35028
-
M. I.Weinstein, "Modulational stability of ground states of nonlinear Schrödinger equations", SIAM J. Math. Anal. 16:3 (1985), 472-491. MR 86i:35130 Zbl 0583.35028
-
(1985)
SIAM J. Math. Anal.
, vol.16
, Issue.3
, pp. 472-491
-
-
Weinstein, M.I.1
|