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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 27969, 14 pages

On a singular sublinear polyharmonic problem

Département de Mathematiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 1060, Tunisia

Received 27 June 2005; Accepted 5 September 2005

Copyright © 2006 Sonia Ben Othman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with a class of singular nonlinear polyharmonic equations on the unit ball B in n (n2) 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)mu=φ(,u)+ψ(,u) in B (in the sense of distributions), u>0, lim|x|1u(x)/(1|x|)m1=0. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions.