A nonexistence result for a nonlinear equation involving critical Sobolev exponent

A. Carpio Rodriguez; M. Comte; R. Lewandowski

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

  • Volume: 9, Issue: 3, page 243-261
  • ISSN: 0294-1449

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Carpio Rodriguez, A., Comte, M., and Lewandowski, R.. "A nonexistence result for a nonlinear equation involving critical Sobolev exponent." Annales de l'I.H.P. Analyse non linéaire 9.3 (1992): 243-261. <http://eudml.org/doc/78278>.

@article{CarpioRodriguez1992,
author = {Carpio Rodriguez, A., Comte, M., Lewandowski, R.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {semilinear elliptic equations; concentration compactness principle; critical Sobolev exponents; moving plane principle},
language = {eng},
number = {3},
pages = {243-261},
publisher = {Gauthier-Villars},
title = {A nonexistence result for a nonlinear equation involving critical Sobolev exponent},
url = {http://eudml.org/doc/78278},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Carpio Rodriguez, A.
AU - Comte, M.
AU - Lewandowski, R.
TI - A nonexistence result for a nonlinear equation involving critical Sobolev exponent
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 3
SP - 243
EP - 261
LA - eng
KW - semilinear elliptic equations; concentration compactness principle; critical Sobolev exponents; moving plane principle
UR - http://eudml.org/doc/78278
ER -

References

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  2. [B] A. Bahri, CriticalPoints at Infinity in Some Variational Problems, Longman, 1989. Zbl0676.58021
  3. [B.C] 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 and Appl. Math., Vol. 41, 1988, pp. 253-294. Zbl0649.35033MR929280
  4. [HB.N] H. Berestycki and L. Nirenberg, Monotonicity, Symmetry and Antisymmetry of Solutions of Semilinear Elliptic Equations, Journal of geometry and physics (to appear). Zbl0698.35031MR1029429
  5. [B.K] H. Brézis and T. Kato, Remarks on the Schrödinger Operator with Singular Complex Potential, Journal maths pures et appl., Vol. 58, 1979, pp. 137-151. Zbl0408.35025MR539217
  6. [B.P] H. Brézis and L.A. Peletier, Asymptotics for Elliptic Equations Involving Critical Growth, Partial Differential Equations and the Calculus of Variations: Essays in honor of E. DeGiori, F. COLOMBINI et al. Eds., Birkhauser, 1989. Zbl0685.35013MR1034005
  7. [D1] E.N. Dancer, On a Nonlinear Elliptic Equation Involving Critical Sobolev Exponent (to appear). 
  8. [D2] W.Y. Ding, Positive Solutions of -Δu=u(N+2)/(N-2) on Contractile Domains (to appear). MR1027983
  9. [G.N.N.] B. Gidas, W.M. Ni and L. Nirenberg, Symmetry and Related Properties via the Maximum Principle, Comm. Math. Phys., Vol. 68, 1979, pp. 209-243. Zbl0425.35020MR544879
  10. [P.L.L] P.L. Lions, The Concentration Compactness Principle in the Calculus of Variations, the Limit Case, Rev. Mat. Iberoamericana, Vol. 1, 1985, pp. 145-201. Zbl0704.49005MR834360
  11. [R.L] R. Lewandowski, Little Holes and Convergence of Solutions of — Δu=u(N+2)/(N-2), Journ. of nonlinear analysisT.M.A., Vol. 14, n° 10, 1990, pp. 873-888. Zbl0713.35008MR1055535
  12. [P] S. Pohozaev, Eigenfunctions of the Equation Δu+λf(u)=0, Dokl. Akad. Nauk S.S.S.R., Vol. 165, 1965, pp. 33-36. Zbl0141.30202MR192184
  13. [S] J. Serrin, A Symmetry Problem in Potential Theory, Arch. Rational Mech. Anal., Vol. 43, 1971, pp. 304-318. Zbl0222.31007MR333220

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