@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 DA - 1994/// SP - 343 EP - 356 VL - Ser. 4, 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 -
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. http://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. | MR 929280 | Zbl 0649.35033
- ,[2] Isoperimetric inequalities and applications. Monographs and Studies in Mathematics, Pitman Advanced Publishing Program, Pitman Publishing Limited, London, 1980. | MR 572958 | Zbl 0436.35063
,[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. | MR 861481 | Zbl 0601.35043
,[4] Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477. | MR 709644 | Zbl 0541.35029
- ,[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 0249.35029
,[6] Symmetry and related properties via the maximal principle, Comm. Math. Phys., 68 (1979), 209-243. | MR 544879 | Zbl 0425.35020
- - ,[7] A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations, 6 (1981), 883-901. | MR 619749 | Zbl 0462.35041
- ,[8] Elliptic partial differential equations of second order, Springer-Verlag, New York, 1982 (second edition). | MR 737190 | Zbl 0562.35001
- ,[9] Rearrangement and convexity of level sets in PDE, Lecture Notes in Mathematics (1150), Springer-Verlag, New York, 1985. | MR 810619 | Zbl 0593.35002
,[10] Uniqueness of positive solutions of Δu - u + up = 0 in R n, Arch. Rational Mech. Anal., 105 (1989), 243-266. | Zbl 0676.35032
,[11] Uniqueness of positive radial solutions of Δu + f(u) = 0 in Rn, Arch. Rational Mech. Anal., 99 (1987), 115-145. | Zbl 0667.35023
- ,[12] Uniqueness and non-uniqueness for positive radial solutions of Δu + f(u, r) = 0, Comm. Pure Appl. Math., 38 (1985), 67-108. | Zbl 0581.35021
- ,[13] Uniqueness of non-negative solutions of semilinear equations in Rn, J. Differential Equations, 61 (1986), 380-397. | MR 829369 | Zbl 0577.35035
- ,[14] Eigenfunctions of the equation Δu + λf(u) = 0, Dokl. Akad. Nauk SSSR, 165 (1956), 1408-1410. | Zbl 0141.30202
,[15] Minimax method in critical point theory with applications to differential equations. CBMS Regional Con. Series Math., no. 65, AMS, Providence, 1986. | MR 845785 | Zbl 0609.58002
,[16] Best constant in Sobolev inequality. Ann. Mat. Pura Appl., 110 (1976), 353-372. | MR 463908 | Zbl 0353.46018
,[17] Variational methods for eigenvalue approximation. Regional conference series in applied mathematics, SIAM, Philadelphia, 1974. | MR 400004 | Zbl 0296.49033
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