Van Schaftingen [@SV] by minimizing the corresponding energy functional. In their paper $\mathcal{W}(x_{1,\,{\varepsilon}})\rightarrow
 sup_{x\in\Omega}\mathcal{W}(x)$. Even in the case $m=1$, our result extends theirs to general critical points (with additional assumption that the critical point is non-degenerate). The method used in [@SV] can not be applied to deal with general critical point cases. The method used here is constructive and is completely different from theirs.

In this case that $m=1$ suppose that $x_1$ is a strict local maximum(or minimum) point of Kirchhoff-Routh function $\mathcal{W}(x)$ defined by , statement of Theorem \[nth1\] still holds which can be proved similarly(see Remark \[re1.4\]). Thus we can obtain corresponding existence result in [@SV].

Theorem \[nth1\] is proved via considering the following problem $$\label{0}
\begin{cases}
-{\varepsilon}^2 \Delta u=\sum_{j=1}^m \chi_{{\Omega}_j}(u-q-\frac{\kappa_j}{2\pi}\ln\frac{1}{{\varepsilon}})_+^p, \quad & x\in\Omega, \\
u=0, \quad & x\in\partial\Omega,
\end{cases}$$ where $p>1$, $q\in C^2(\Omega)$, $\Omega\subset\mathbb{R}^2$ is a bounded domain, ${\Omega}_j\subset\Omega$ is a subdomain such that $x^*_j\in{\Omega}_j,\,j=1,\cdots,m$ and ${\Omega}_i\cap{\Omega}_j={\O}$ if $ i\neq
j$.

\[th3\]

Suppose $q\in C^2(\Omega)$. For $\kappa_i>0,~i=1,\cdots,m$. Then, for any given $C^1$-stable critical point $(x_1^*,\cdots,x_m^*)$ of Kirchhoff-Routh function $\mathcal{W}(x_1,\cdots,x_m)$ defined by , there exists ${\varepsilon}_0>0$, such that for each ${\varepsilon}\in (0,{\varepsilon}_0)$, has a solution $u_{\varepsilon}$, such that the set $\Omega_{{\varepsilon},i} =\{x:
u_{\varepsilon}(x)-\frac{\kappa_i}{2\pi}\,\ln\frac{1}{{\varepsilon}}-q(x)>0\}\subset\subset{\Omega}_i,
\,i=1,2,\cdots,m$ and each $\Omega_{{\varepsilon},\,i}$ shrinks 