On a variational problem with lack of compactness: the topological effect of the critical points at infinity

@article{Bahri1995OnAV,
  title={On a variational problem with lack of compactness: the topological effect of the critical points at infinity},
  author={A. Bahri and Yanyan Li and O. Rey},
  journal={Calculus of Variations and Partial Differential Equations},
  year={1995},
  volume={3},
  pages={67-93}
}
  • A. Bahri, Yanyan Li, O. Rey
  • Published 1995
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
    • RésuméNous étudions les problèmes sous-critiquesPɛ:−Δu=up−ɛ,u > 0 surΩ;u=0 sur ∂Ω−oùΩ est un domaine borné et régulier de ℝN,N−3,p + 1=2N/N −2 est l'exposant critique de Sobolev, et ɛ>0 tend vers zéro, afin de calculer la différence de toplogie induite par les points critiques à l'infini entre les ensembles de niveau de la fonctionnelle correspondant au cas limite (P0).AbstractWe study the subcritical problemsPɛ:−Δu=up−ɛ,u>0 onΩ;u=0 on ∂Ω,ω being a smooth and bounded domain in ℝN,N−3,p+1=2N/N−2… CONTINUE READING
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    References

    SHOWING 1-10 OF 49 REFERENCES
    On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
    • 614
    • Highly Influential
    The role of the green's function in a non-linear elliptic equation involving the critical Sobolev exponent
    • 410
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    Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
    • 2,125
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    A global compactness result for elliptic boundary value problems involving limiting nonlinearities
    • 576
    A Note on an Equation with Critical Exponent
    • 101
    Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
    • 904
    • PDF
    The Concentration-Compactness Principle in the Calculus of Variations. (The limit case, Part I.)
    • 1,467
    Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent
    • 21
    Conformal deformation of a Riemannian metric to constant scalar curvature
    • 974
    • PDF
    Symmetry of positive solutions of nonlinear elliptic equations in R
    • 1,028
    • PDF