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Abstract and Applied Analysis
Volume 2007, Article ID 56981, 16 pages
Research Article

Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball

Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia

Received 27 October 2006; Accepted 9 April 2007

Academic Editor: Jean-Pierre Gossez

Copyright © 2007 Sonia Ben Othman et al. 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.


Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in n(n2)()mu+g(,u)=0, in B (in the sense of distributions) limxξB(u(x)/(1|x|2)m1)=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.