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On a singular sublinear polyharmonic problem

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  • Sonia Ben Othman

Abstract

This paper deals with a class of singular nonlinear polyharmonic equations on the unit ball B in ℝ n ( n ≥ 2 ) where the combined effects of a singular and a sublinear term allow us by using the Schauder fixed point theorem to establish an existence result for the following problem: ( − Δ ) m u = φ ( ⋅ , u ) + ψ ( ⋅ , u ) in B (in the sense of distributions), u > 0 , lim ⁡ | x | → 1 u ( x ) / ( 1 − | x | ) m − 1 = 0 . Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions.

Suggested Citation

  • Sonia Ben Othman, 2006. "On a singular sublinear polyharmonic problem," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-14, May.
    • Handle: RePEc:hin:jnlaaa:027969
    DOI: 10.1155/AAA/2006/27969
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