Abstract and Applied Analysis
Volume 2003 (2003), Issue 12, Pages 715-741
doi:10.1155/S1085337503209039
Estimates for the Green function and singular solutions for polyharmonic nonlinear equation
Imed Bachar
, Habib Màagli
, Syrine Masmoudi
and Malek Zribi
Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 1060, Tunisia
Abstract
We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of ℝn(n≥2) 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.