Abstract and Applied Analysis
Volume 2006 (2006), Article ID 89491, 22 pages
Estimates for the green function and existence of positive solutions for higher-order elliptic equations
Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia
Received 7 March 2005; Accepted 7 April 2005
Copyright © 2006 Imed Bachar. 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.
We establish a -theorem for the iterated Green function of , (), on the unit ball of with boundary conditions on , for and . We exploit this
result to study a class of potentials . Next, we aim at proving the existence of positive continuous
solutions for the following polyharmonic nonlinear problems , in (in the sense of distributions), , for , where or and is a Borel measurable
function on satisfying some appropriate
conditions related to .