Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent

Zheng-Chao Han

Annales de l'I.H.P. Analyse non linéaire (1991)

  • Volume: 8, Issue: 2, page 159-174
  • ISSN: 0294-1449

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Han, Zheng-Chao. "Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent." Annales de l'I.H.P. Analyse non linéaire 8.2 (1991): 159-174. <http://eudml.org/doc/78248>.

@article{Han1991,
author = {Han, Zheng-Chao},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular solutions; critical Sobolev exponent},
language = {eng},
number = {2},
pages = {159-174},
publisher = {Gauthier-Villars},
title = {Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent},
url = {http://eudml.org/doc/78248},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Han, Zheng-Chao
TI - Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 2
SP - 159
EP - 174
LA - eng
KW - singular solutions; critical Sobolev exponent
UR - http://eudml.org/doc/78248
ER -

References

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  1. [AP] F. Atkinson and L. Peletier, Elliptic Equations with Nearly Critical Growth, J. Diff. Eq., vol. 70, 1987, pp. 349-365. Zbl0657.35058MR915493
  2. [BC] A. Bahri and J. Coron, On a Nonlinear Elliptic Equation Involving the Critical Sobolev Exponent: the Effect of the Topology of the Domain, Comm. Pure Appl. Math., vol. 41, 1988, pp. 253-294. Zbl0649.35033MR929280
  3. [BP] H. Brezis and L. Peletier, Asymptotics for Elliptic Equations Involving Critical Growth (to appear). Zbl0685.35013MR1034005
  4. [CGS] L. Caffarelli, B. Gidas and J. Spuck, Asymptotic Symmetry and Local Behavior of Semilinear Elliptic Equations with Critical Growth, Comm. Pure Appl. Math., vol. 42, 1989, p. 271-297. Zbl0702.35085MR982351
  5. [DLN] D.G. De Figueiredo, P.L. Lions and R.D. Nussbaum, A priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations, J. Math. Pures Appl., vol. 61, 1982, pp. 41-63. Zbl0452.35030MR664341
  6. [D] W. Ding, Positive Solutions of Δu + u(n + 2)/(n - 2) = 0 on a Contractible Domain, preprint. MR1027983
  7. [GNN] B. Gidas, W. Ni and L. Nirenberg, Symmetry and Related Properties via the Maximum Principle, Comm. Math. Phys., vol. 68, 1979, pp. 209-243. Zbl0425.35020MR544879
  8. [GT] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 2nd ed, New York, 1983. Zbl0562.35001MR737190
  9. [P] S. Pohozaev, Eigenfunctions of the Equations Δu=λf(u), Soviet Math. Dokl., vol. 6, 1965, pp. 1408-1411. 
  10. [R1] O. Rey, The Role of the Green's Function in a Nonlinear Elliptic Equation Involving the Critical Sobolev Exponent, Funct. Anal., 1990 (to appear). Zbl0786.35059MR1040954
  11. [R2] O. Rey, A Multiplicity Result for a Variational Problem with Lack of Compactness, J. Nonlinear Analysis, T.M.A., vol. 133, No. 10, 1989, pp. 1241-1249. Zbl0702.35101MR1020729
  12. [R3] O. Rey, Proof of Two Conjectures of H. Brezis and L. A. Peletier, Manuscripta math., vol. 65, 1989, pp. 19-37. Zbl0708.35032MR1006624
  13. [SU] J. Sacks and K. Uhlenbeck, The Existence of Minimal Immersions of 2-Spheres, Ann. Math., vol. 113, 1981, pp. 1-24. Zbl0462.58014MR604040
  14. [S] M. Struwe, A Global Compactness Result for Elliptic Boundary Value Problems Involving Limiting Nonlinearities, Math. Z., vol. 187, 1984, pp. 511-517. Zbl0535.35025MR760051

Citations in EuDML Documents

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  1. Riccardo Molle, Donato Passaseo, Positive solutions of slightly supercritical elliptic equations in symmetric domains
  2. Monica Musso, Angela Pistoia, Persistence of Coron’s solution in nearly critical problems
  3. Katiuscia Cerqueti, Un risultatodi unicità per un’equazione semilineare ellittica con esponente critico in domini simmetrici
  4. Olivier Druet, Elliptic equations with critical Sobolev exponents in dimension 3
  5. Emmanuel Hebey, Michel Vaugon, Meilleures constantes dans le théorème d'inclusion de Sobolev
  6. Angela Pistoia, Tobias Weth, Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
  7. Micol Amar, Adriana Garroni, Γ -convergence of concentration problems
  8. Giampiero Palatucci, Subcritical approximation of the Sobolev quotient and a related concentration result
  9. I. A. Guerra, Solutions of an elliptic system with a nearly critical exponent
  10. Olivier Rey, Elliptic equations with limiting Sobolev exponent: the impact of the Green's function

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