On a singular sublinear polyharmonic problem

Sonia Ben Othman

Abstract and Applied Analysis, 2006, vol. 2006, 1-14

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:027969

DOI: 10.1155/AAA/2006/27969

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