Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 33, pp. 1-11.

Title: Existence of solutions for a sublinear system of elliptic equations  

Author: Carlos Cid    (Univ. de Chile, Santiago, Chile)
        Cecilia Yarur (Univ. de Santiago de Chile, Santiago, Chile)
         
Abstract: 
 We study the existence of non-trivial non-negative
 solutions for the system
 $$ \displaylines{
    -\Delta u  = |x|^av^p \cr
     \Delta v  = |x|^bu^q\,,
 }$$
 where $p$ and $q$ are positive constants with $pq<1$, and the domain is the
 unit ball of $R^N$ ($N>2$) except for the center zero.
 We look for pairs of functions that satisfy the above system and Dirichlet
 boundary conditions set to zero. Our results  also apply to some super-linear
 systems.

Submitted January 21, 2000. Published May 9, 2000.
Math Subject Classifications: 35A20, 35J60, 34B18.
Key Words: Semilinear elliptic systems; sub-harmonic functions; 
           super-harmonic functions