It is well known that the least energy solution of the Lane-Emden system

 

 ,  ,

 

blow-up at a point as p = (N+2)/(N-2) −  goes to the critical exponent. Also there are many results about the multi-bubbling phenomena of the Lane-Emden equation near the critical exponent. However, the blow-up scenario of the Lane-Emden system is more complicated than that of the classical Lane-Emden equation because of the strong nonlinear characteristic of the system. In this talk, we will study previous results for the Lane-Emden equation and introduce our results for the system.