@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},
year = {1994},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 21},
number = {3},
zbl = {0815.35031},
language = {en},
url = {https://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 - https://www.numdam.org/item/ASNSP_1994_4_21_3_343_0/ 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 %U https://www.numdam.org/item/ASNSP_1994_4_21_3_343_0/ %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, Série 4, Tome 21 (1994) no. 3, pp. 343-356. https://www.numdam.org/item/ASNSP_1994_4_21_3_343_0/
[1] - , 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. | Zbl | MR
[2] , Isoperimetric inequalities and applications. Monographs and Studies in Mathematics, Pitman Advanced Publishing Program, Pitman Publishing Limited, London, 1980. | Zbl | MR
[3] , 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. | Zbl | MR
[4] - , Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477. | Zbl | MR
[5] , 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] - - , Symmetry and related properties via the maximal principle, Comm. Math. Phys., 68 (1979), 209-243. | Zbl | MR
[7] - , A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations, 6 (1981), 883-901. | Zbl | MR
[8] - , Elliptic partial differential equations of second order, Springer-Verlag, New York, 1982 (second edition). | Zbl | MR
[9] , Rearrangement and convexity of level sets in PDE, Lecture Notes in Mathematics (1150), Springer-Verlag, New York, 1985. | Zbl | MR
[10] , Uniqueness of positive solutions of Δu - u + up = 0 in R n, Arch. Rational Mech. Anal., 105 (1989), 243-266. | Zbl
[11] - , Uniqueness of positive radial solutions of Δu + f(u) = 0 in Rn, Arch. Rational Mech. Anal., 99 (1987), 115-145. | Zbl
[12] - , Uniqueness and non-uniqueness for positive radial solutions of Δu + f(u, r) = 0, Comm. Pure Appl. Math., 38 (1985), 67-108. | Zbl
[13] - , Uniqueness of non-negative solutions of semilinear equations in Rn, J. Differential Equations, 61 (1986), 380-397. | Zbl | MR
[14] , Eigenfunctions of the equation Δu + λf(u) = 0, Dokl. Akad. Nauk SSSR, 165 (1956), 1408-1410. | Zbl
[15] , Minimax method in critical point theory with applications to differential equations. CBMS Regional Con. Series Math., no. 65, AMS, Providence, 1986. | Zbl | MR
[16] , Best constant in Sobolev inequality. Ann. Mat. Pura Appl., 110 (1976), 353-372. | Zbl | MR
[17] , Variational methods for eigenvalue approximation. Regional conference series in applied mathematics, SIAM, Philadelphia, 1974. | Zbl | MR





