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Manuscripta Mathematica

, Volume 137, Issue 3–4, pp 525–544 | Cite as

A priori estimates for superlinear and subcritical elliptic equations: the Neumann boundary condition case

  • Abdellaziz Harrabi
  • Mohameden Ould AhmedouEmail author
  • Salem Rebhi
  • Abdelbaki Selmi
Article

Abstract

We consider here solutions of a nonlinear Neumann elliptic equation Δuf (x, u) = 0 in Ω, ∂u/∂ν = 0 on ∂Ω, where Ω is a bounded open smooth domain in \({\mathbb{R}^N, N\geq2}\) and f satisfies super-linear and subcritical growth conditions. We prove that L −bounds on solutions are equivalent to bounds on their Morse indices.

Mathematics Subject Classification (2000)

35J60 35J65 58E05 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Abdellaziz Harrabi
    • 1
  • Mohameden Ould Ahmedou
    • 2
    Email author
  • Salem Rebhi
    • 3
  • Abdelbaki Selmi
    • 4
  1. 1.Département de MathématiquesInstitue de Mathématiques Appliquées et d’Informatiques de KairouanKairouanTunisia
  2. 2.Tübingen UniversityTübingenGermany
  3. 3.Département de Mathématiques, Faculté des Sciences deTunisUniversity ElmanarTunisTunisia
  4. 4.Département de MathématiquesFaculté des Sciencesde BizerteBizerteTunisia

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