Standing waves for nonlinear Schrödinger equations with singular potentials
Jaeyoung Byeon; Zhi-Qiang Wang
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 3, page 943-958
- ISSN: 0294-1449
Access Full Article
topHow to cite
topByeon, Jaeyoung, and Wang, Zhi-Qiang. "Standing waves for nonlinear Schrödinger equations with singular potentials." Annales de l'I.H.P. Analyse non linéaire 26.3 (2009): 943-958. <http://eudml.org/doc/78875>.
@article{Byeon2009,
author = {Byeon, Jaeyoung, Wang, Zhi-Qiang},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear Schrödinger equations; singularities of potentials; decaying and unbounded potentials},
language = {eng},
number = {3},
pages = {943-958},
publisher = {Elsevier},
title = {Standing waves for nonlinear Schrödinger equations with singular potentials},
url = {http://eudml.org/doc/78875},
volume = {26},
year = {2009},
}
TY - JOUR
AU - Byeon, Jaeyoung
AU - Wang, Zhi-Qiang
TI - Standing waves for nonlinear Schrödinger equations with singular potentials
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 3
SP - 943
EP - 958
LA - eng
KW - nonlinear Schrödinger equations; singularities of potentials; decaying and unbounded potentials
UR - http://eudml.org/doc/78875
ER -
References
top- [1] Ambrosetti A., Felli V., Malchiodi A., Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. Eur. Math. Soc.7 (2005) 117-144. Zbl1064.35175MR2120993
- [2] Ambrosetti A., Malchiodi A., Perturbation Methods and Semilinear Elliptic Problems on , Progress in Mathematics, vol. 240, Birkhäuser Verlag, Basel, 2006. Zbl1115.35004MR2186962
- [3] Ambrosetti A., Malchiodi A., Ni W.-M., Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, I, Commun. Math. Phys.235 (2003) 427-466. Zbl1072.35019MR1974510
- [4] Ambrosetti A., Malchiodi A., Ruiz D., Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. d'Analyse Math.98 (2006) 317-348. Zbl1142.35082MR2254489
- [5] Ambrosetti A., Ruiz D., Radial solutions concentrating on spheres of NLS with vanishing potentials, preprint, Proc. Roy. Soc. Edinburgh Sect. A136 (2006) 889-907. Zbl1126.35059MR2266391
- [6] Ambrosetti A., Wang Z.-Q., Nonlinear Schrödinger equations with vanishing and decaying potentials, Differential Integral Equations18 (2005) 1321-1332. Zbl1210.35087MR2174974
- [7] Byeon J., Jeanjean L., Standing waves for nonlinear Schrödinger equations with a general nonlinearity, Arch. Ration. Mech. Anal.185 (2007) 185-200. Zbl1132.35078MR2317788
- [8] Byeon J., Oshita Y., Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations, Comm. Partial Differential Equations29 (2004) 1877-1904. Zbl1088.35062MR2106071
- [9] Byeon J., Wang Z.-Q., Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal.165 (2002) 295-316. Zbl1022.35064MR1939214
- [10] Byeon J., Wang Z.-Q., Standing waves with a critical frequency for nonlinear Schrödinger equations, II, Cal. Var. Partial Differential Equations18 (2003) 207-219. Zbl1073.35199MR2010966
- [11] Byeon J., Wang Z.-Q., Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials, J. Eur. Math. Soc.8 (2006) 217-228. Zbl1245.35036MR2239273
- [12] Caffarelli L., Kohn R., Nirenberg L., First order interpolation inequalities with weights, Compositio Math.53 (1984) 259-275. Zbl0563.46024MR768824
- [13] Dancer E.N., Yan S., On the existence of multipeak solutions for nonlinear field equations on , Discrete Contin. Dynam. Systems6 (2000) 39-50. Zbl1157.35367MR1739592
- [14] Del Pino M., Felmer P.L., Semi-classical states for nonlinear Schrödinger equations: A variational reduction method, Math. Ann.324 (2002) 1-32. Zbl1030.35031MR1931757
- [15] Floer A., Weinstein A., Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal.69 (1986) 397-408. Zbl0613.35076MR867665
- [16] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, second ed., Springer, Berlin, 1983. Zbl0562.35001MR737190
- [17] Kang X., Wei J., On interacting bumps of semi-classical states of nonlinear Schrödinger equations, Adv. Differential Equations5 (2000) 899-928. Zbl1217.35065MR1776345
- [18] Lieb E.H., Seiringer R., Proof of Bose–Einstein condensation for dilute trapped gases, Phys. Rev. Lett.88 (2002) 170409. Zbl1041.81107
- [19] Meystre P., Atom Optics, Springer, 2001.
- [20] Mills D.L., Nonlinear Optics, Springer, 1998. Zbl0914.00011
- [21] Rabinowitz P.H., On a class of nonlinear Schrödinger equations, ZAMP43 (1992) 270-291. Zbl0763.35087MR1162728
- [22] Wang X., Zeng B., On concentration of positive bound states of nonlinear Schrödinger equations with competing potential functions, SIAM J. Math. Anal.28 (1997) 633-655. Zbl0879.35053MR1443612
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.