Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger-Poisson systems in $\mathbb {R}^3$

Benmlih, Khalid; Kavian, Otared

Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger-Poisson systems in

ℝ^{3}

Benmlih, Khalid ; Kavian, Otared

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 449-470 / Harvested from Numdam

Access to full text
Full (PDF)
Full (DJVU)

Publié le : 2008-01-01

MR 2422075 | Zbl pre05290957

DOI : https://doi.org/10.1016/j.anihpc.2007.02.002

@article{AIHPC_2008__25_3_449_0,
     author = {Benmlih, Khalid and Kavian, Otared},
     title = {Existence and asymptotic behaviour of standing waves for quasilinear Schr\"odinger-Poisson systems in $\mathbb {R}^3$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {449-470},
     doi = {10.1016/j.anihpc.2007.02.002},
     mrnumber = {2422075},
     zbl = {pre05290957},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_3_449_0}
}

Benmlih, Khalid; Kavian, Otared. Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger-Poisson systems in $\mathbb {R}^3$. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 449-470. doi : 10.1016/j.anihpc.2007.02.002. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_3_449_0/

Bibliographie

[1] Akhmediev N., Ankiewicz A., Soto-Crespo J.M., Does the nonlinear Schrödinger equation correctly describe beam propagation?, Optics Lett. 18 (1993) 411-413.

[2] Kh. Benmlih, Stationary solutions for a Schrödinger-Poisson system in $R^{3}$ , Electron. J. Differential Equations, Proceedings of Conf. 09 (2002), pp. 65-76. http://www.emis.de/journals/EJDE/. | MR 1976685 | Zbl 1109.35373

[3] Benmlih Kh., A note on a 3-dimensional stationary Schrödinger-Poisson system, Electron. J. Differential Equations 2004 (26) (2004) 1-5. | MR 2036210 | Zbl pre02100267

[4] Brezis H., Kato T., Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl. 58 (2) (1979) 137-151. | MR 539217 | Zbl 0408.35025

[5] Gilbard D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[6] Hauss H.A., Waves and Fields in Optoelectronics, Prentice-Hall, Englewood Cliffs, NJ, 1984.

[7] Illner R., Kavian O., Lange H., Stationary solutions of quasi-linear Schrödinger-Poisson systems, J. Differential Equations 145 (1998) 1-16. | MR 1620258 | Zbl 0909.35133

[8] Illner R., Lange H., Toomire B., Zweifel P.F., On quasi-linear Schrödinger-Poisson systems, Math. Meth. Appl. Sci. 20 (1997) 1223-1238. | MR 1468411 | Zbl 0886.35125

[9] Kavian O., Introduction à la Théorie des Points Critiques, Springer-Verlag, Berlin, 1993. | MR 1276944

[10] Lions J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. | MR 259693 | Zbl 0189.40603

[11] Lions P.L., The concentration-compactness principle in the calculus of variations, the limit case, Part 1, Rev. Mat. Iberoamericana 1 (1985) 145-201. | MR 834360 | Zbl 0704.49005

[12] Lions P.L., Some remarks on Hartree equations, Nonlinear Anal. 5 (1981) 1245-1256. | MR 636734 | Zbl 0472.35074

[13] Markowich P.A., Ringhofer C., Schmeiser C., Semiconductor Equations, Springer, Wien, 1990. | MR 1063852 | Zbl 0765.35001

[14] Maz'Ja V.G., Sobolev Spaces, Springer, Berlin, 1985.

[15] Struwe M., Variational Methods, Application to Nonlinear PDE & Hamiltonian Systems, second ed., Springer, Berlin, 1996. | Zbl 0864.49001