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Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball

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  • Sonia Ben Othman
  • Habib Mâagli
  • Malek Zribi

Abstract

Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in ℝ n ( n ≥ 2 ) ( − △ ) m u + g ( ⋅ , u ) = 0 , in B (in the sense of distributions) lim x → ξ ∈ ∂ B ( u ( x ) / ( 1 − | x | 2 ) m − 1 ) = 0 ( ξ ) . Under appropriate conditions related to a Kato class on the nonlinearity g ( x , t ) , we give some existence results. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions, including a 3G-theorem, which leeds to some useful properties on functions belonging to the Kato class.

Suggested Citation

  • Sonia Ben Othman & Habib Mâagli & Malek Zribi, 2007. "Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball," Abstract and Applied Analysis, Hindawi, vol. 2007, pages 1-16, May.
    • Handle: RePEc:hin:jnlaaa:056981
    DOI: 10.1155/2007/56981
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