Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field
Annales de l'I.H.P. Physique théorique, Volume 54 (1991) no. 4, p. 403-433
@article{AIHPA_1991__54_4_403_0,
author = {Gon\c calves Ribeiro, J. M.},
title = {Instability of symmetric stationary states for some nonlinear Schr\"odinger equations with an external magnetic field},
journal = {Annales de l'I.H.P. Physique th\'eorique},
publisher = {Gauthier-Villars},
volume = {54},
number = {4},
year = {1991},
pages = {403-433},
zbl = {0741.35080},
mrnumber = {1128864},
language = {en},
url = {http://www.numdam.org/item/AIHPA_1991__54_4_403_0}
}

Gonçalves Ribeiro, J. M. Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field. Annales de l'I.H.P. Physique théorique, Volume 54 (1991) no. 4, pp. 403-433. http://www.numdam.org/item/AIHPA_1991__54_4_403_0/

[1] H. Berestycki a4cnd T. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon nonlinéaires, C.R. Acad. Sci. Paris, T. 293, 1981, pp. 489-492. | MR 646873 | Zbl 0492.35010

[2] H. Berestycki and P.L. Lions, Nonlinear Scalar Field Equations. I, Arch. Rat. Mech. Anal., Vol. 82, 1983, pp. 313-345. | MR 695535 | Zbl 0533.35029

[3] P. Blanchard, J. Stubbe and L. Vasquez, On the Stability of Solitary Waves for Classical Scalar Fields, Ann. Inst. Henri-Poincaré, Phys. Théor., Vol. 47, 1987, pp. 309-336. | Numdam | MR 921309 | Zbl 0649.35076

[4] T. Cazenave, An Introduction to Nonlinear Schödinger Equations, Textos de Métodos Matemáticos. No. 22, I.M.U.F.R.J., Rio de Janeiro, 1989.

[5] T. Cazenave and M. Esteban, On the Stability of Stationary States for Nonlinear Schrödinger Equations with an External Magnetic Field, Mat. Apl. Comp., Vol. 7, 1988, pp. 155-168. | MR 994761 | Zbl 0681.35011

[6] T. Cazenave and P.L. Lions, Orbital Stability of Standing Waves for some Nonlinear Schrödinger Equations, Comm. Math. Phys., Vol. 85, 1982, pp. 549-561. | MR 677997 | Zbl 0513.35007

[7] M. Esteban and P.L. Lions, Stationnary Solutions of Nonlinear Schrödinger Equations with an External Magnetic Field. In Partial Differential Equations and the Calculus of Variations, F. COLOMBINI et al. Eds., Birkhäuser, Boston, 1989, pp. 401-409. | MR 1034014 | Zbl 0702.35067

[8] Gonçalves Ribeiro, Finite Time Blow-up for Some Nonlinear Schrödinger Equations with an External Magnetic Field (to appear). | Zbl 0734.35127

[9] M. Grillakis, J. Shatah and W.A. Strauss, Stability Theory of Solitary Waves in the Presence of Symmetry. I, J. Funct. Anal., Vol. 74, 1987, pp. 160-197. | MR 901236 | Zbl 0656.35122

[10] P. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986. | MR 836734 | Zbl 0588.22001

[11] J. Shatah, Stable Standing Waves of Nonlinear Klein-Gordon Equations, Comm. Math. Phys., Vol. 91, 1983, pp. 313-327. | MR 723756 | Zbl 0539.35067

[12] J. Shatah, Unstable Ground States of Nonlinear Klein-Gordon Equations, Trans. Am. Math. Soc., Vol. 290, 1985, pp. 701-710. | MR 792821 | Zbl 0617.35072

[13] J. Shatah and W.A. Strauss, Instability of Nonlinear Bound States, Comm. Math. Phys., Vol. 100, 1985, pp. 173-190. | MR 804458 | Zbl 0603.35007

[14] W.A. Strauss, Existence of Solitary Waves in Higher Dimensions, Comm. Math. Phys., Vol. 55, 1977, pp. 149-162. | MR 454365 | Zbl 0356.35028

[15] J. Stubbe, Linear Stability Theory of Solitary Waves arising from Hamiltonian Systems with Symmetry, Portug. Math., Vol. 46, 1989, pp. 17-32. | MR 996398 | Zbl 0687.35088

[16] M. Weinstein, Liapounov Stability of Ground States of Nonlinear Dispersive Evolution Equations, Comm. Pure Appl. Math., Vol. 39, 1968, pp. 51-67. | MR 820338 | Zbl 0594.35005