Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 81, pp. 1-13.

Title: Existence of continuous positive solutions for some 
       nonlinear polyharmonic systems outside the unit ball
       
Author: Sameh Turki (Faculte des Sciences de Tunis, Tunisia)

Abstract:
 We study the existence of continuous positive solutions of the
 m-polyharmonic nonlinear elliptic system
 $$\displaylines{
 (-\Delta)^{m}u+\lambda p(x)g(v)=0,\cr
 (-\Delta )^{m}v+\mu q(x)f(u)=0
 }$$
 in the complement of the unit closed ball in $\mathbb{R}^{n}$
 (n>2m and $m\geq 1$). Here the constants $\lambda,\mu$ are
 nonnegative, the functions f,g are nonnegative, continuous and
 monotone. We prove two  existence results  for the above system
 subject to some boundary conditions, where the nonnegative
 functions p,q satisfy some appropriate conditions related
 to a Kato class of functions.

Submitted May 23, 2011. Published June 21, 2011.
Math Subject Classifications: 34B27, 35J40.
Key Words: Polyharmonic elliptic system; Positive solutions; 
           Green function; polyharmonic Kato class.