A Remark on the Generalized Second Order Toda System

In this paper, we establish a priori estimates to the generalized second order Toda system{-Δu1(x)=2R1(x)eu1-R2eu2,-Δu2(x)=R1(x)eu1+2R2eu2 in R2 , and discuss the convergence and asymptotic behavior of its solutions, where Ri(x), i=1, 2, is bounded function in R2 . Consequently, we prove that all the solutions satisfy an identity, which is somewhat a generalization of the well-known Kazdan-Warner condition.