On the number of single-peak solutions of the nonlinear Schrödinger equation
Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 3, p. 261-280
@article{AIHPC_2002__19_3_261_0,
author = {Grossi, Massimo},
title = {On the number of single-peak solutions of the nonlinear Schr\"odinger equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {19},
number = {3},
year = {2002},
pages = {261-280},
zbl = {1034.35127},
mrnumber = {1956951},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2002__19_3_261_0}
}

Grossi, Massimo. On the number of single-peak solutions of the nonlinear Schrödinger equation. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 3, pp. 261-280. http://www.numdam.org/item/AIHPC_2002__19_3_261_0/

[1] Ambrosetti A., Badiale M., Cingolani S., Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal. 140 (1997) 285-300. | MR 1486895 | Zbl 0896.35042

[2] Cao D., Noussair E., Yan S., Existence and uniqueness results on single peaked solutions of a semilinear problem, Ann. Inst. H. Poincaré 15 (1998) 73-111. | Numdam | MR 1614607 | Zbl 0905.35033

[3] Dancer E.N., On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mountain J. Math. 25 (1995) 957-975. | MR 1357103 | Zbl 0846.35046

[4] Del Pino M., Felmer P.L., Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. PDE 149 (1997) 245-265. | MR 1471107 | Zbl 0887.35058

[5] Del Pino M., Felmer P.L., Semiclassical states of nonlinear Schrödinger equations, J. Funct. Anal. 149 (1997) 245-265. | MR 1471107 | Zbl 0887.35058

[6] Ding W.Y., Ni W.M., On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Rat. Mech. Anal. 91 (1986) 283-308. | MR 807816 | Zbl 0616.35029

[7] 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

[8] Grossi M., Some results for a class of nonlinear Schrödinger equations, Math. Z. 235 (2000) 687-705. | MR 1801580 | Zbl 0970.35039

[9] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in RN, in: Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Studies, 7A, Academic Press, New York, 1981. | MR 634248 | Zbl 0469.35052

[10] Gilbarg D., Trudinger N., Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. | MR 473443 | Zbl 0361.35003 | Zbl 1042.35002

[11] Kwong M.K., Uniqueness of positive solutions of Δuu+up=0 in Rn, Arch. Rat. Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032

[12] Li Y.Y., On a singularly perturbed elliptic equation, Adv. Diff. Eqns. 2 (1997) 955-980. | MR 1606351 | Zbl 1023.35500

[13] Lloyd, Degree Theory, Cambridge University Press. | MR 493564 | Zbl 0367.47001

[14] Ni W.M., Takagi I., On the shape of least energy solutions to a semilinear Neumann problem, Comm. Pure Math. Appl. 41 (1991) 819-851. | MR 1115095 | Zbl 0754.35042

[15] Ni W.M., Wei J., On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Math. Appl. 48 (1995) 731-768. | MR 1342381 | Zbl 0838.35009

[16] Oh Y.G., Existence of semiclassical bound states of nonlinear Schrödinger equation with potential in the class (V)α, Comm. Part. Diff. Eq. 13 (1988) 1499-1519. | MR 970154 | Zbl 0702.35228

[17] Rabinowitz P., On a class of nonlinear Schrödinger equation, Z. Angew. Math. Phys. 43 (1992) 270-291. | MR 1162728 | Zbl 0763.35087

[18] Wang X., On a concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153 (1993) 223-243. | MR 1218300 | Zbl 0795.35118