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On the effect of the domain geometry on uniqueness of positive solutions of Δ u + u p = 0

Henghui Zou

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 3, page 343-356
  • ISSN: 0391-173X

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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 21.3 (1994): 343-356. <http://eudml.org/doc/84181>.

@article{Zou1994,
author = {Zou, Henghui},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {uniqueness of positive solutions; semilinear elliptic equation},
language = {eng},
number = {3},
pages = {343-356},
publisher = {Scuola normale superiore},
title = {On the effect of the domain geometry on uniqueness of positive solutions of $\Delta u + u^p = 0$},
url = {http://eudml.org/doc/84181},
volume = {21},
year = {1994},
}

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
PB - Scuola normale superiore
VL - 21
IS - 3
SP - 343
EP - 356
LA - eng
KW - uniqueness of positive solutions; semilinear elliptic equation
UR - http://eudml.org/doc/84181
ER -

References

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  2. [2] C. Bandle, Isoperimetric inequalities and applications. Monographs and Studies in Mathematics, Pitman Advanced Publishing Program, Pitman Publishing Limited, London, 1980. Zbl0436.35063MR572958
  3. [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. Zbl0601.35043MR861481
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  5. [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. Zbl0249.35029
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  8. [8] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, New York, 1982 (second edition). Zbl0562.35001MR737190
  9. [9] B. Kawohl, Rearrangement and convexity of level sets in PDE, Lecture Notes in Mathematics (1150), Springer-Verlag, New York, 1985. Zbl0593.35002MR810619
  10. [10] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in R n, Arch. Rational Mech. Anal., 105 (1989), 243-266. Zbl0676.35032
  11. [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. Zbl0667.35023
  12. [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. Zbl0581.35021
  13. [13] L.A. Peletier - J. Serrin, Uniqueness of non-negative solutions of semilinear equations in Rn, J. Differential Equations, 61 (1986), 380-397. Zbl0577.35035MR829369
  14. [14] S.I. Pohozaev, Eigenfunctions of the equation Δu + λf(u) = 0, Dokl. Akad. Nauk SSSR, 165 (1956), 1408-1410. Zbl0141.30202
  15. [15] P. Rabinowitz, Minimax method in critical point theory with applications to differential equations. CBMS Regional Con. Series Math., no. 65, AMS, Providence, 1986. Zbl0609.58002MR845785
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  17. [17] H. Weinberger, Variational methods for eigenvalue approximation. Regional conference series in applied mathematics, SIAM, Philadelphia, 1974. Zbl0296.49033MR400004

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