Standing Waves for Nonlinear Schrödinger Equations With Singular Potentials
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, p. 943-958
@article{AIHPC_2009__26_3_943_0,
     author = {Byeon, Jaeyoung and Wang, Zhi-Qiang},
     title = {Standing Waves for Nonlinear Schr\"odinger Equations With Singular Potentials},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {3},
     year = {2009},
     pages = {943-958},
     doi = {10.1016/j.anihpc.2008.03.009},
     zbl = {1177.35215},
     mrnumber = {2526410},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_3_943_0}
}
Byeon, Jaeyoung; Wang, Zhi-Qiang. Standing Waves for Nonlinear Schrödinger Equations With Singular Potentials. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, pp. 943-958. doi : 10.1016/j.anihpc.2008.03.009. http://www.numdam.org/item/AIHPC_2009__26_3_943_0/

[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. | MR 2120993 | Zbl 1064.35175

[2] Ambrosetti A., Malchiodi A., Perturbation Methods and Semilinear Elliptic Problems on R n , Progress in Mathematics, vol. 240, Birkhäuser Verlag, Basel, 2006. | MR 2186962 | Zbl 1115.35004

[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. | MR 1974510 | Zbl 1072.35019

[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. | MR 2254489 | Zbl 1142.35082

[5] Ambrosetti A., Ruiz D., Radial Solutions Concentrating on Spheres of NLS With Vanishing Potentials, Preprint, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907. | MR 2266391 | Zbl 1126.35059

[6] Ambrosetti A., Wang Z.-Q., Nonlinear Schrödinger Equations With Vanishing and Decaying Potentials, Differential Integral Equations 18 (2005) 1321-1332. | MR 2174974

[7] Byeon J., Jeanjean L., Standing Waves for Nonlinear Schrödinger Equations With a General Nonlinearity, Arch. Ration. Mech. Anal. 185 (2007) 185-200. | MR 2317788 | Zbl 1132.35078

[8] Byeon J., Oshita Y., Existence of Multi-Bump Standing Waves With a Critical Frequency for Nonlinear Schrödinger Equations, Comm. Partial Differential Equations 29 (2004) 1877-1904. | MR 2106071 | Zbl 1088.35062

[9] Byeon J., Wang Z.-Q., Standing Waves With a Critical Frequency for Nonlinear Schrödinger Equations, Arch. Ration. Mech. Anal. 165 (2002) 295-316. | MR 1939214 | Zbl 1022.35064

[10] Byeon J., Wang Z.-Q., Standing Waves With a Critical Frequency for Nonlinear Schrödinger Equations, II, Cal. Var. Partial Differential Equations 18 (2003) 207-219. | MR 2010966 | Zbl 1073.35199

[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. | MR 2239273 | Zbl pre05053360

[12] Caffarelli L., Kohn R., Nirenberg L., First Order Interpolation Inequalities With Weights, Compositio Math. 53 (1984) 259-275. | Numdam | MR 768824 | Zbl 0563.46024

[13] Dancer E. N., Yan S., On the Existence of Multipeak Solutions for Nonlinear Field Equations on R n , Discrete Contin. Dynam. Systems 6 (2000) 39-50. | MR 1739592 | Zbl 1157.35367

[14] Del Pino M., Felmer P. L., Semi-Classical States for Nonlinear Schrödinger Equations: a Variational Reduction Method, Math. Ann. 324 (2002) 1-32. | MR 1931757 | Zbl 1030.35031

[15] Floer A., Weinstein A., Nonspreading Wave Packets for the Cubic Schrödinger Equation With a Bounded Potential, J. Funct. Anal. 69 (1986) 397-408. | MR 867665 | Zbl 0613.35076

[16] Gilbarg D., Trudinger N. S., Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, second ed., Springer, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[17] Kang X., Wei J., On Interacting Bumps of Semi-Classical States of Nonlinear Schrödinger Equations, Adv. Differential Equations 5 (2000) 899-928. | MR 1776345 | Zbl pre01700753

[18] Lieb E. H., Seiringer R., Proof of Bose-Einstein Condensation for Dilute Trapped Gases, Phys. Rev. Lett. 88 (2002) 170409.

[19] Meystre P., Atom Optics, Springer, 2001.

[20] Mills D. L., Nonlinear Optics, Springer, 1998. | Zbl 0914.00011

[21] Rabinowitz P. H., On a Class of Nonlinear Schrödinger Equations, ZAMP 43 (1992) 270-291. | MR 1162728 | Zbl 0763.35087

[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. | MR 1443612 | Zbl 0879.35053