Concentration of solutions to elliptic equations with critical nonlinearity

O. Rey

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 2, page 201-218
  • ISSN: 0294-1449

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Rey, O.. "Concentration of solutions to elliptic equations with critical nonlinearity." Annales de l'I.H.P. Analyse non linéaire 9.2 (1992): 201-218. <http://eudml.org/doc/78276>.

@article{Rey1992,
author = {Rey, O.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {existence of solutions; blow-up; variational problems with lack of compactness; limiting Sobolev exponent; Dirichlet boundary conditions},
language = {eng},
number = {2},
pages = {201-218},
publisher = {Gauthier-Villars},
title = {Concentration of solutions to elliptic equations with critical nonlinearity},
url = {http://eudml.org/doc/78276},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Rey, O.
TI - Concentration of solutions to elliptic equations with critical nonlinearity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 2
SP - 201
EP - 218
LA - eng
KW - existence of solutions; blow-up; variational problems with lack of compactness; limiting Sobolev exponent; Dirichlet boundary conditions
UR - http://eudml.org/doc/78276
ER -

References

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  1. [B] A. Bahri, Critical Points at Infinity in Some Variational Problems, Pitman Research Notes in Mathematics Series, No. 182, Longman, 1989. Zbl0676.58021
  2. [BC] A. Bahri and J.-M. Coron, On a Nonlinear Elliptic Equation Involving the Critical Sobolev Exponent: the Effect of the Topology of the Domain, Comm. Pure Applied Math., Vol. 41, 1988, pp. 255-294. Zbl0649.35033
  3. [BN1] H. Brézis and L. Nirenberg, Positive Solutions of Nonlinear Equations Involving Critical Sobolev Exponents, Comm. Pure Applied Math., Vol. 36, 1983, pp.437-477. Zbl0541.35029MR709644
  4. [BN2] H. Brézis and L. Nirenberg, A Minimization Problem with Critical Exponent and Nonzero Data (to appear). Zbl0763.46023
  5. [BP] H. Brézis and L.A. Peletier, Asymptotics for Elliptic Equations Involving Critical Growth, Partial Differential Equations and the Calculus of Variations, F. COLOMBANI, L. MODICA and S. SPAGNOLO Eds., Birkhauser, 1989. Zbl0685.35013MR1034005
  6. [H] Z.C. Han, Asymptotic Approach to Singular Solutions for Nonlinear Elliptic Equations Involving Critical Sobolev Exponent (to appear). Zbl0729.35014MR1096602
  7. [P] S. Pohozaev, Eigenfunctions of the Equation Δu = λf(u), Soviet Math. Dokl., Vol. 6, 1965, pp. 1408-1411. 
  8. [R1] O. Rey, The Role of Green's function in a Nonlinear Elliptic Equation Involving the Critical Sobolev Exponent, J. Funct. Analysis, Vol. 89, No. 1, 1990, pp. 1-52. Zbl0786.35059MR1040954
  9. [R2] O. Rey, A Multiplicity Result for a Variational Problem with Lack of Compactness, J. Nonlinear Anal. T.M.A., Vol. 13, No. 10, 1989, pp. 1241-1249. Zbl0702.35101MR1020729
  10. [R3] O. Rey, Proof of Two Conjectures of H. Brézis and L. A. Peletier, Manuscripta Math., Vol. 65, 1989, pp. 19-37. Zbl0708.35032MR1006624
  11. [R4] O. Rey, Bifurcation from Infinity in a Nonlinear Elliptic Equation Involving the Limiting Sobolev Exponent, Duke Math. Journal., Vol. 60, 1990, pp. 815-861. Zbl0711.35012MR1054534

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