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.
@article{AIHPA_1991__54_4_403_0,
     author = {Gon\c{c}alves 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},
     pages = {403--433},
     publisher = {Gauthier-Villars},
     volume = {54},
     number = {4},
     year = {1991},
     mrnumber = {1128864},
     zbl = {0741.35080},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1991__54_4_403_0/}
}
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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://archive.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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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