@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}, volume = {19}, year = {2002}, pages = {261-280}, mrnumber = {1956951}, zbl = {1034.35127}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 19 (2002) pp. 261-280. http://gdmltest.u-ga.fr/item/AIHPC_2002__19_3_261_0/
[1] Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal. 140 (1997) 285-300. | MR 1486895 | Zbl 0896.35042
, , ,[2] 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] 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] Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. PDE 149 (1997) 245-265. | MR 1471107 | Zbl 0887.35058
, ,[5] Semiclassical states of nonlinear Schrödinger equations, J. Funct. Anal. 149 (1997) 245-265. | MR 1471107 | Zbl 0887.35058
, ,[6] 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] 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] Some results for a class of nonlinear Schrödinger equations, Math. Z. 235 (2000) 687-705. | MR 1801580 | Zbl 0970.35039
,[9] 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] Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. | MR 473443 | Zbl 0361.35003 | Zbl 1042.35002
, ,[11] Uniqueness of positive solutions of Δu−u+up=0 in Rn, Arch. Rat. Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032
,[12] 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] 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] 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] 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] On a class of nonlinear Schrödinger equation, Z. Angew. Math. Phys. 43 (1992) 270-291. | MR 1162728 | Zbl 0763.35087
,[18] On a concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153 (1993) 223-243. | MR 1218300 | Zbl 0795.35118
,