Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in R 3

Khalid Benmlih; Otared Kavian

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 3, page 449-470
  • ISSN: 0294-1449

How to cite

top

Benmlih, Khalid, and Kavian, Otared. "Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in ${R}^{3}$." Annales de l'I.H.P. Analyse non linéaire 25.3 (2008): 449-470. <http://eudml.org/doc/78797>.

@article{Benmlih2008,
author = {Benmlih, Khalid, Kavian, Otared},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Schrödinger equation; Poisson equation; standing wave solutions; variational methods; asymptotic behaviour},
language = {eng},
number = {3},
pages = {449-470},
publisher = {Elsevier},
title = {Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in $\{R\}^\{3\}$},
url = {http://eudml.org/doc/78797},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Benmlih, Khalid
AU - Kavian, Otared
TI - Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in ${R}^{3}$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 3
SP - 449
EP - 470
LA - eng
KW - Schrödinger equation; Poisson equation; standing wave solutions; variational methods; asymptotic behaviour
UR - http://eudml.org/doc/78797
ER -

References

top
  1. [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. [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/. Zbl1109.35373MR1976685
  3. [3] Benmlih Kh., A note on a 3-dimensional stationary Schrödinger–Poisson system, Electron. J. Differential Equations2004 (26) (2004) 1-5. Zbl1217.35059MR2036210
  4. [4] Brezis H., Kato T., Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl.58 (2) (1979) 137-151. Zbl0408.35025MR539217
  5. [5] Gilbard D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer, Berlin, 1983. Zbl0562.35001MR737190
  6. [6] Hauss H.A., Waves and Fields in Optoelectronics, Prentice-Hall, Englewood Cliffs, NJ, 1984. 
  7. [7] Illner R., Kavian O., Lange H., Stationary solutions of quasi-linear Schrödinger–Poisson systems, J. Differential Equations145 (1998) 1-16. Zbl0909.35133MR1620258
  8. [8] Illner R., Lange H., Toomire B., Zweifel P.F., On quasi-linear Schrödinger–Poisson systems, Math. Meth. Appl. Sci.20 (1997) 1223-1238. Zbl0886.35125MR1468411
  9. [9] Kavian O., Introduction à la Théorie des Points Critiques, Springer-Verlag, Berlin, 1993. Zbl0797.58005MR1276944
  10. [10] Lions J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. Zbl0189.40603MR259693
  11. [11] Lions P.L., The concentration-compactness principle in the calculus of variations, the limit case, Part 1, Rev. Mat. Iberoamericana1 (1985) 145-201. Zbl0704.49005MR834360
  12. [12] Lions P.L., Some remarks on Hartree equations, Nonlinear Anal.5 (1981) 1245-1256. Zbl0472.35074MR636734
  13. [13] Markowich P.A., Ringhofer C., Schmeiser C., Semiconductor Equations, Springer, Wien, 1990. Zbl0765.35001MR1063852
  14. [14] Maz'ja V.G., Sobolev Spaces, Springer, Berlin, 1985. 
  15. [15] Struwe M., Variational Methods, Application to Nonlinear PDE & Hamiltonian Systems, second ed., Springer, Berlin, 1996. Zbl0864.49001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.