@article{AIHPC_1998__15_1_73_0, author = {Cao, Dao-Min and Noussair, Ezzat S. and Yan, Shusen}, title = {Existence and uniqueness results on Single-Peaked solutions of a semilinear problem}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {15}, year = {1998}, pages = {73-111}, mrnumber = {1614607}, zbl = {0905.35033}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1998__15_1_73_0} }
Cao, Daomin; Noussair, Ezzat S.; Yan, Shusen. Existence and uniqueness results on Single-Peaked solutions of a semilinear problem. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) pp. 73-111. http://gdmltest.u-ga.fr/item/AIHPC_1998__15_1_73_0/
[1] On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain. Comm. Pure. appl. Math., Vol. 41, 1988, pp. 253-294. | MR 929280 | Zbl 0649.35033
and ,[2] On a variational problem with lack of compactness: the topological effect of the critical points at infinity. Cal. Var., Vol. 3, 1995, pp. 67-93. | MR 1384837 | Zbl 0814.35032
, ,[3] The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems. Arch. Rational Mech. Anal., 114, 1994, pp. 79-93. | MR 1088278 | Zbl 0727.35055
and ,[4] Solutions with multiple "Peaks" for nonlinear elliptic equations, preprint. | MR 1686700
, and ,[5] The effect of the domain shape on the number of positive solutions of certain equations, J. Diff. Equs., Vol. 74, 1988, pp. 316-339. | Zbl 0662.34025
,[6] The effect of the domain shape on the number of positive solutions of certain nonlinear equations, II, J. Diff. Equa., Vol. 87, 1990, pp. 316-339. | MR 1072904 | Zbl 0729.35050
,[7] WEI-MING NI, and L. NIRENBERG, Symmetry and related properties via the maximum principle, Comm. Math. Phys., Vol. 68, 1979, pp. 209-243. | MR 544879 | Zbl 0425.35020
,[8] Uniqueness of positive solutions of a nonlinear elliptic equation involving the critical exponent, Nonlinear Anal. T.M.A., Vol. 20, No. 5, 1993, pp. 571-603. | MR 1207531 | Zbl 0797.35048
,[9] On the location and profile of spike-layer solutions to singularity perturbed semilinear problems, to appear in Comm. Pure Appl. Math.
,[10] On the shape of the least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math., Vol. 44, 1991, pp. 819-851. | MR 1115095 | Zbl 0754.35042
,[11] The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal., Vol. 89, 1990, pp. 1-52. | MR 1040954 | Zbl 0786.35059
,[12] Viscosity approach to the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem, preprint. | MR 1404386
,