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

  • Abbas Bahri
  • Yanyan Li
  • Olivier Rey
Article

Abstract

We study the subcritical problemsP ɛ :−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 the critical Sobolev exponent and ɛ>0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P0).

Mathematics subject classification

35J65 

Résumé

Nous étudions les problèmes sous-critiquesP ɛ :−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).

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Abbas Bahri
    • 1
    • 2
  • Yanyan Li
    • 2
  • Olivier Rey
    • 1
  1. 1.Ecole PolytechniqueCentre de MathématiquesPalaiseau CedexFrance
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

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