point. Then in section five, for local equations we use Pohozaev identity to determine the locations of blowup points. Then in section six we return to the equation on manifold and compute the leading term for $\rho^k\to \rho$ in both situations ($\rho\neq Q$ or $\rho=Q$) and complete the proofs of the main theorems.

[**Acknowledgement**]{} Part of the paper was finished when the second author was visiting Taida Institute for Mathematical Sciences (TIMS) in March 2011 and June 2012. He is very grateful to TIMS for their warm hospitality. He also would like to thank the National Science Foundation for the partial support (NSF-DMS-1027628).

Preliminary results on the Liouville systems
============================================

In this section we prove two theorems on the Liouville systems with the matrix $A$ satisfying $(H1)$. They are important for the blowup analysis and the computation of the leading terms of $\rho\to \Gamma_1$ in this paper and $\rho\to \Gamma_N$ in the forthcoming work [@linzhang4].

A uniqueness theorem for the linearized system of $n$ equations
---------------------------------------------------------------

In the first subsection we prove a uniqueness theorem for the linearized system of $n$ equations.

\[uniqlin\] Let $A$ be a matrix that satisfies (H1), $u=(u_1,..,u_n)$ be a radial solution of $$\left\{\begin{array}{ll}
-\Delta u_i=\sum_{j=1}^na_{ij}e^{u_j}\,\, 