A remark on the generalized second order Toda system

作者：Pei Rui Chang^*

来源：Acta Mathematica Sinica-English Series, 2013, 29(9): 1691-1702.

DOI：10.1007/s10114-013-2080-9

• Second order Toda system
• asymptotic behavior
• priori estimates
• convergence

In this paper, we establish a priori estimates to the generalized second order Toda system
{-Delta u(1)(x) = 2R(1)(x)e(u1) - R(2)e(u2),
-Delta u(2)(x) = -R-1(x)e(u1) + 2R(2)e(u2)
in R-2, and discuss the convergence and asymptotic behavior of its solutions, where R-i (x), i = 1, 2, is bounded function in R-2. Consequently, we prove that all the solutions satisfy an identity, which is somewhat a generalization of the well-known Kazdan-Warner condition.

• 出版日期2013-9
• 单位天水师范学院