Asymptotics for ${L}^{2}$ minimal blow-up solutions of critical nonlinear Schrödinger equation
Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 5, pp. 553-565.
@article{AIHPC_1996__13_5_553_0,
author = {Merle, Frank},
title = {Asymptotics for $L^2$ minimal blow-up solutions of critical nonlinear {Schr\"odinger} equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {553--565},
publisher = {Gauthier-Villars},
volume = {13},
number = {5},
year = {1996},
zbl = {0862.35013},
mrnumber = {1409662},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1996__13_5_553_0/}
}
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Merle, Frank. Asymptotics for $L^2$ minimal blow-up solutions of critical nonlinear Schrödinger equation. Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 5, pp. 553-565. http://archive.numdam.org/item/AIHPC_1996__13_5_553_0/

[1] H. Berestycki and P.L. Lions, Nonlinear scalar field equations I. Existence of a ground state; II. Existence of infinitely many solutions, Arch. Rational Mech. Anal., Vol. 82, 1983, pp. 313-375. | MR | Zbl

[2] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations I, II. The Cauchy problem, general case, J. Funct. Anal., Vol. 32, 1979, pp. 1-71. | MR | Zbl

[3] T. Kato, On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 49, 1987, pp. 113-129. | Numdam | MR | Zbl

[4] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in RN, Arch. Rational Mech. Anal., Vol. 105, 1989, pp. 243-266. | MR | Zbl

[5] F. Merle, Determination of blow-up solutions with minimal mass for Schrödinger equation with critical power, Duke J., Vol. 69, 1993, pp. 427-454. | MR | Zbl

[6] F. Merle, Nonexistence of minimal blow-up solutions of equations iut = -Δu - k(x)|u|4/Nu in RN, preprint.

[7] W.A. Strauss, Existence of solitary waves in higher dimensions, Commun. Math. Phys., Vol. 55, 1977, pp. 149-162. | MR | Zbl

[8] M.I. Weinstein, Modulational stability of ground states of the nonlinear Schrödinger equations, SIAM J. Math. Anal., Vol. 16, 1985, pp. 472-491. | MR | Zbl

[9] M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys., Vol. 87, 1983, pp. 567-576. | MR | Zbl