no. 5
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) no. 5, pp. 631-652. 
@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},
     pages = {631--652},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     mrnumber = {1712564},
     zbl = {0935.35049},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_5_631_0/}
}
TY  - JOUR
AU  - Damascelli, Lucio
AU  - Grossi, Massimo
AU  - Pacella, Filomena
TI  - Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1999
SP  - 631
EP  - 652
VL  - 16
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1999__16_5_631_0/
LA  - en
ID  - AIHPC_1999__16_5_631_0
ER  - 
%0 Journal Article
%A Damascelli, Lucio
%A Grossi, Massimo
%A Pacella, Filomena
%T Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 631-652
%V 16
%N 5
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1999__16_5_631_0/
%G en
%F 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) no. 5, pp. 631-652. http://www.numdam.org/item/AIHPC_1999__16_5_631_0/

[1] Adimurthi, F. Pacella and S. Yadava, On the number of positive solutions of some semilinear Dirichlet problems in a ball, Diff. Int. Eq., Vol. 10, 1997, pp. 1157-1170. | MR | Zbl

[2] Adimurthi and S. Yadava, 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 | Zbl

[3] A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex

nonlinearities in some elliptic problems, J. Funct. Anal., Vol. 122, 1994, pp. 519-543. | MR | Zbl

[4] A. Babin, Symmetry of instability for scalar equations in symmetric domains, J. Diff. Eq.Vol. 123, 1995, pp. 122-152. | MR | Zbl

[5] H. Berestycki and L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat., Vol. 22, 1991, pp. 1-37. | MR | Zbl

[6] H. Berestycki, L. Nirenberg and S.N.S. Varadhan, 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 | Zbl

[7] H. Brezis and S. Kamin, Sublinear elliptic equations in RN, Man. Math., Vol. 74, 1992,pp. 87-106. | MR | Zbl

[8] L. Damascelli, 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 | Zbl

[9] E.N. Dancer, 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

[10] B. Gidas, W.M. Ni and L. Nirenberg, Symmetry and related properties via the maximum

principle, Comm. Math. Phis., Vol. 68, 1979, pp. 209-243. | MR | Zbl

[11] B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic

equations, Comm. Par. Diff. Eq., Vol. 6, 1981, pp. 883-901. | Zbl

[12] D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, 1983. | MR | Zbl

[13] C.S. Lin, Uniqueness of solutions minimizing the functional ∫Ω |∇u|2/(∫Ω|u|p+1)2/(p+1) in R2 (preprint). | MR

[14] C.S. Lin and W.M. Ni, A counterexample to the nodal domain conjecture and a related

semilinear equation, Proc. Amer. Mat. Soc., Vol. 102, 1988, pp. 271-277. | MR | Zbl

[15] W.N. Ni and R.D. Nussbaum, 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

[16] M.H. Protter and H.F. Weinberger, Maximum principle in differential equations, Prentice Hall, Englewoood Cliffs, New Jersey, 1967. | MR | Zbl

[17] P.N. Srikanth, Uniqueness of solutions of nonlinear Dirichlet problems, Diff. Int. Eq., Vol. 6, 1993, pp. 663-670. | MR | Zbl

[18] Liqun Zhang, Uniqueness of positive solutions of Δu + u + up = 0 in a finite ball, Comm. Part. Diff. Eq., Vol. 17, 1992, pp. 1141-1164. | MR | Zbl

[19] Liqun Zhang, Uniqueness of positive solutions of Δu + up = 0 in a convex domain in R2, (preprint).

[20] H. Zou, 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 | Zbl