@article{AIHPC_1999__16_5_631_0, author = {Damascelli, Lucio and Grossi, Massimo and Pacella, Filomena}, title = {Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {16}, year = {1999}, pages = {631-652}, mrnumber = {1712564}, zbl = {0935.35049}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1999__16_5_631_0} }
Damascelli, Lucio; Grossi, Massimo; Pacella, Filomena. Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) pp. 631-652. http://gdmltest.u-ga.fr/item/AIHPC_1999__16_5_631_0/
[1] On the number of positive solutions of some semilinear Dirichlet problems in a ball, Diff. Int. Eq., Vol. 10, 1997, pp. 1157-1170. | MR 1608057 | Zbl 0940.35069
, and ,[2] An elementary proof for the uniqueness of positive radial solution of a quasilinear Dirichlet problem, Arch. Rat. Mech. Anal., Vol. 126, 1994,pp. 219-229. | MR 1288602 | Zbl 0806.35031
and ,[3] Combined effects of concave and convex
, and ,nonlinearities in some elliptic problems, J. Funct. Anal., Vol. 122, 1994, pp. 519-543. | MR 1276168 | Zbl 0805.35028
[4] Symmetry of instability for scalar equations in symmetric domains, J. Diff. Eq.Vol. 123, 1995, pp. 122-152. | MR 1359914 | Zbl 0852.35069
,[5] On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat., Vol. 22, 1991, pp. 1-37. | MR 1159383 | Zbl 0784.35025
and ,[6] The principle eigenvalues and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math., Vol. 47, 1994, pp. 47-92. | MR 1258192 | Zbl 0806.35129
, and ,[7] Sublinear elliptic equations in RN, Man. Math., Vol. 74, 1992,pp. 87-106. | MR 1141779 | Zbl 0761.35027
and ,[8] A remark on the uniqueness of the positive solution for a semilinear
,elliptic equation, Nonlin. Anal. T.M.A., Vol. 26, 1996, pp. 211-216. | MR 1359470 | Zbl 0838.35041
[9] The effect of domain shape on the number of positive solutions of certain
,nonlinear equations, J. Diff. Eq., Vol. 74, 1988, pp. 120-156. | Zbl 0662.34025
[10] Symmetry and related properties via the maximum
, and ,principle, Comm. Math. Phis., Vol. 68, 1979, pp. 209-243. | MR 544879 | Zbl 0425.35020
[11] A priori bounds for positive solutions of nonlinear elliptic
and ,equations, Comm. Par. Diff. Eq., Vol. 6, 1981, pp. 883-901. | Zbl 0462.35041
[12] Elliptic partial differential equations of second order, Springer Verlag, 1983. | MR 737190 | Zbl 0562.35001
and ,[13] Uniqueness of solutions minimizing the functional ∫Ω |∇u|2/(∫Ω|u|p+1)2/(p+1) in R2 (preprint). | MR 1283323
,[14] A counterexample to the nodal domain conjecture and a related
and ,semilinear equation, Proc. Amer. Mat. Soc., Vol. 102, 1988, pp. 271-277. | MR 920985 | Zbl 0652.35085
[15] Uniqueness and non-uniqueness for positive radial solutions of Δu + f(u, r) = 0, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 67-108. | Zbl 0581.35021
and ,[16] Maximum principle in differential equations, Prentice Hall, Englewoood Cliffs, New Jersey, 1967. | MR 219861 | Zbl 0153.13602
and ,[17] Uniqueness of solutions of nonlinear Dirichlet problems, Diff. Int. Eq., Vol. 6, 1993, pp. 663-670. | MR 1202564 | Zbl 0803.35057
,[18] Uniqueness of positive solutions of Δu + u + up = 0 in a finite ball, Comm. Part. Diff. Eq., Vol. 17, 1992, pp. 1141-1164. | MR 1179281 | Zbl 0782.35025
,[19] Uniqueness of positive solutions of Δu + up = 0 in a convex domain in R2, (preprint).
,[20] On the effect of the domain geometry on uniqueness of positive solutions of Δu + up = 0, Ann. Sc. Nor. Sup., 1995, pp. 343-356. | Numdam | MR 1310630 | Zbl 0815.35031
,