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Abstract and Applied Analysis
Volume 2003 (2003), Issue 12, Pages 715-741
http://dx.doi.org/10.1155/S1085337503209039

Estimates for the Green function and singular solutions for polyharmonic nonlinear equation

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

Received 5 July 2002

Copyright © 2003 Hindawi Publishing Corporation. 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.

Abstract

We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of n(n2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions Km,n containing properly the classical Kato class Kn. We exploit properties of functions belonging to Km,n to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order 2m.