Let Ω be a bounded domain in $\mathbb{R}^2 $ with smooth boundary, we study the following Neumann boundary value problem
$\left\{ \begin{gathered} \begin{gathered} - \Delta \upsilon + \upsilon = 0\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\text{in}}\;\;\Omega {\text{,}} \hfill \\ \frac{{\partial \upsilon }}{{\partial \nu }} = {e^\upsilon } - s{\phi _1} - h\left( x \right)\;\;\;{\text{on}}\;\partial \Omega \hfill \\ \end{gathered} \end{gathered} \right.$
where $ν$ denotes the outer unit normal vector to $\partial \Omega$ , $h∈ C^{0,α}(\partial \Omega)$ , $s>0$ is a large parameter and $\phi_1$ is a positive first Steklov eigenfunction. We construct solutions of this problem which exhibit multiple boundary concentration behavior around maximum points of $\phi_1$ on the boundary as $s\to+∞$ .
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