The Hénon-Lane-Emden conjecture predicts nonexistence of positive entire solutions of a weighted elliptic system in its subcritical range. For 
,
positive exponents 
, and real weights 
, the classical formulation uses solutions continuous
on 
and twice continuously differentiable away from the origin. The system is
 |
The subcritical condition is
 |
The unweighted case 
is the Lane-Emden system. This coupled system is different
from the radial scalar Lane-Emden
differential equation.
