A Remark on the Generalized Second Order Toda System  

作　　者：Rui Chang PEI 

机构地区：[1]School of Mathematics and Statistics, Tianshui Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第9期1691-1702,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10671156)

摘　　要：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.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.

关 键 词：Second order Toda system asymptotic behavior priori estimates CONVERGENCE 

分 类 号：O175[理学—数学]