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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 153, Issue 1, pp 191–201 | Cite as

Solutions d'équations elliptiques semi-linéaires singulières

  • Robert Dalmasso
Article

Résumé

Récemment T.Kusanoet C. A.Swansonont étudié l'équation elliptique semilinéaireΔu+j(x)uλ=0,xRn,n⩾ 3et 0</λ</ l.Ils ont montré l'existence d'une solution positive globale se comportant comme ¦x¦2−n pour ¦x¦ grand. Nous démontrons l'existence et l'unicité d'une telle solution pour λ >/ 0.

Summary

T.Kusano and C. A.Swanson have recently studied the semilinear elliptic equationΔu+j(x)uλ=0,xRn,n⩾3 and 0<λ < 1. They have shown the existence of a global positive solution behaving like ¦x¦2−n for large ¦x¦. We establish the existence and uniqueness of such a solution when λ > 0.

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Bibliographie

  1. [1]
    K. Akô -T. Kusano,On bounded solutions of second order elliptic differential equations, J. Fac. Sci. Univ. Tokyo, Sect. I,11 (1964), pp. 29–37.MathSciNetMATHGoogle Scholar
  2. [2]
    J.Dieudonné,Eléments d'analyse, tome II, Gauthier-Villars, Paris.Google Scholar
  3. [3]
    T. Kusano -C. A. Swanson,Entire positive solutions of singular semilinear elliptic equations, Japan J. Math.,11, no. 1 (1985), pp. 145–155.MathSciNetMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1989

Authors and Affiliations

  • Robert Dalmasso
    • 1
  1. 1.EchirollesFrance

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