A Liouville theorem for subcritical Lane-Emden system
  In this paper, we present a necessary and sufficient condition to the Lane-Emden conjecture. This condition is an energy type of integral estimate on solutions to subcritical Lane-Emden system. To approach the long standing and interesting conjecture, we believe that one plausible path is to refocus on establishing this energy type estimate. 
Ze Cheng, Genggeng Huang, Congming Li
math.AP