no. 3
On the effect of the domain geometry on uniqueness of positive solutions of Δu+u p =0
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 21 (1994) no. 3, pp. 343-356. 
@article{ASNSP_1994_4_21_3_343_0,
     author = {Zou, Henghui},
     title = {On the effect of the domain geometry on uniqueness of positive solutions of $\Delta u + u^p = 0$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {343--356},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 21},
     number = {3},
     year = {1994},
     zbl = {0815.35031},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1994_4_21_3_343_0/}
}
TY  - JOUR
AU  - Zou, Henghui
TI  - On the effect of the domain geometry on uniqueness of positive solutions of $\Delta u + u^p = 0$
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1994
SP  - 343
EP  - 356
VL  - 21
IS  - 3
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1994_4_21_3_343_0/
UR  - https://zbmath.org/?q=an%3A0815.35031
LA  - en
ID  - ASNSP_1994_4_21_3_343_0
ER  - 
%0 Journal Article
%A Zou, Henghui
%T On the effect of the domain geometry on uniqueness of positive solutions of $\Delta u + u^p = 0$
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1994
%P 343-356
%V 21
%N 3
%I Scuola normale superiore
%G en
%F ASNSP_1994_4_21_3_343_0
Zou, Henghui. On the effect of the domain geometry on uniqueness of positive solutions of $\Delta u + u^p = 0$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 21 (1994) no. 3, pp. 343-356. http://www.numdam.org/item/ASNSP_1994_4_21_3_343_0/

[1] A. Bahri - J.M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent, the effect of the topology of the domain. Comm. Pure Appl. Math. 41 (1988), 253-294. | MR | Zbl

[2] C. Bandle, Isoperimetric inequalities and applications. Monographs and Studies in Mathematics, Pitman Advanced Publishing Program, Pitman Publishing Limited, London, 1980. | MR | Zbl

[3] H. Brezis, Elliptic equations with limit Sobolev exponents - the impact of topology, Frontier of the mathematical sciences (New York, 1985). Comm. Pure Appl. Math., 39 (1986), no. S, suppl., S17-S39. | MR | Zbl

[4] H. Brezis - L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477. | MR | Zbl

[5] C.V. Coffman, Uniqueness of the ground state solution for Δu - u + u3 = 0 and a variational characterization of other solutions, Arch. Rational Mech. Anal., 46 (1972), 81-95. | Zbl

[6] B. Gidas - W.M. Ni - L. Nirenberg, Symmetry and related properties via the maximal principle, Comm. Math. Phys., 68 (1979), 209-243. | MR | Zbl

[7] B. Gidas - J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations, 6 (1981), 883-901. | MR | Zbl

[8] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, New York, 1982 (second edition). | MR | Zbl

[9] B. Kawohl, Rearrangement and convexity of level sets in PDE, Lecture Notes in Mathematics (1150), Springer-Verlag, New York, 1985. | MR | Zbl

[10] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in R n, Arch. Rational Mech. Anal., 105 (1989), 243-266. | Zbl

[11] K. Mcleod - J. Serrin, Uniqueness of positive radial solutions of Δu + f(u) = 0 in Rn, Arch. Rational Mech. Anal., 99 (1987), 115-145. | Zbl

[12] W.M. Ni - R.D. Naussbaum, Uniqueness and non-uniqueness for positive radial solutions of Δu + f(u, r) = 0, Comm. Pure Appl. Math., 38 (1985), 67-108. | Zbl

[13] L.A. Peletier - J. Serrin, Uniqueness of non-negative solutions of semilinear equations in Rn, J. Differential Equations, 61 (1986), 380-397. | MR | Zbl

[14] S.I. Pohozaev, Eigenfunctions of the equation Δu + λf(u) = 0, Dokl. Akad. Nauk SSSR, 165 (1956), 1408-1410. | Zbl

[15] P. Rabinowitz, Minimax method in critical point theory with applications to differential equations. CBMS Regional Con. Series Math., no. 65, AMS, Providence, 1986. | MR | Zbl

[16] G. Talenti, Best constant in Sobolev inequality. Ann. Mat. Pura Appl., 110 (1976), 353-372. | MR | Zbl

[17] H. Weinberger, Variational methods for eigenvalue approximation. Regional conference series in applied mathematics, SIAM, Philadelphia, 1974. | MR | Zbl