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, p. 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},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {5},
     year = {1996},
     pages = {553-565},
     zbl = {0862.35013},
     mrnumber = {1409662},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1996__13_5_553_0}
}
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://www.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 695535 | Zbl 0533.35029

[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 533219 | Zbl 0396.35028

[3] T. Kato, On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 49, 1987, pp. 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[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 969899 | Zbl 0676.35032

[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 1203233 | Zbl 0808.35141

[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 454365 | Zbl 0356.35028

[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 783974 | Zbl 0583.35028

[9] M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys., Vol. 87, 1983, pp. 567-576. | MR 691044 | Zbl 0527.35023