Abstract and Applied Analysis
Volume 2006 (2006), Article ID 76582, 24 pages
doi:10.1155/AAA/2006/76582
Existence of positive solutions for some polyharmonic nonlinear equations in ℝn
Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia
Received 25 December 2004; Accepted 1 March 2005
Copyright © 2006 Habib Mâagli and Malek Zribi. 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 will study the following polyharmonic nonlinear elliptic
equation (−∆)mu+f(‧,u)=0 in ℝn, n>2m.
Under appropriate conditions on the nonlinearity f(x,t), related
to a class of functions called m-Green-tight functions, we give
some existence results for the above equation.