Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials

Journal of the European Mathematical Society

Volumn 8, Issue 2, 2006, Pages 217-228

  Byeon, Jaeyoung ^a   Wang, Zhi Qiang ^b  

^a Pohang University of Science and Technology (POSTECH)   (South Korea)

^b UTAH STATE UNIVERSITY   (United States)

Author keywords

Concentration on spheres; Critical frequency; Nonlinear Schr dinger equations

Indexed keywords

EID: 33745655598     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/48     Document Type: Article

References (16)

1. Ambrosetti, A., Felli, V., Malchiodi, A.: Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Eur. Math. Soc. 7, 117-144 (2005) Zbl 1064.35175 MR 2120993
2. n. Progr. Math. 240, Birkhäuser (2006) Zbl pre05013399 MR 2186962
3. Ambrosetti, A., Malchiodi, A., Ni, W.-M.: Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I. Comm. Math. Phys. 235, 427-466 (2003) Zbl 1072.35019 MR 1974510
4. Ambrosetti, A., Malchiodi, A., Ruiz, D.: Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Anal. Math., to appear
5. Ambrosetti, A., Ruiz, D.: Radial solutions concentrating on spheres of NLS with vanishing potentials. Preprint
6. Ambrosetti, A., Wang, Z.-Q.: Nonlinear Schrödinger equations with vanishing and decaying potentials. Differential Integral Equations 18, 1321-1332 (2005) MR 2174974
7. Bartsch, T., Peng, S.: Semiclassical symmetric Schrödinger equations: existence of solutions concentrating simultaneously on several spheres. Preprint
8. Byeon, J.: Existence of large positive solutions of some nonlinear elliptic equations on singularly perturbed domains. Comm. Partial Differential Equations 22, 1731-1769 (1997) Zbl 0883.35040 MR 1469588
9. Byeon, J., Wang, Z.-Q.: Standing waves with a critical frequency for nonlinear Schrödinger equations. Arch. Rat. Mech. Anal. 165, 295-316 (2002) Zbl 1022.35064 MR 1939214
10. Byeon, J., Wang, Z.-Q.: Standing waves with a critical frequency for nonlinear Schrödinger equations, II. Calc. Van Partial Differential Equations 18, 207-219 (2003) Zbl 1073.35199 MR 2010966
11. Cerami, G., Passaseo, D.: The effect of concentrating potentials in some singularly perturbed problems. Calc. Var. Partial Differential Equations 17, 257-281 (2003) Zbl pre01969061 MR 1989833
12. Dancer, E. N., Yan, S.: A new type of concentration solutions for a singularly perturbed elliptic problem. Preprint
13. Floer, A., Weinstein, A.: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. Funct. Anal. 69, 397-408 (1986) Zbl 0613.35076 MR 0867665
14. Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order. 2nd ed., Grundlehren Math. Wiss. 224, Springer, Berlin (1983) Zbl 0562.35001 MR 0737190
15. Malchiodi, A., Montenegro, M.: Boundary concentration phenomena for a singularly perturbed elliptic problem. Comm. Pure Appl. Math. 55, 1507-1568 (2002) Zbl pre01860559 MR 1923818
16. Molle, R., Passaseo, D.: Concentration phenomena for solutions of superlinear elliptic problems. Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear