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

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.