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In this article we shall study the following elliptic system withcoefficients:  \begin{equation}\notag  \left\{\begin{aligned}  -\epsilon^2\Delta u +c(x)u=b(x)|v|^{q-1}v, &\text{ and } -\epsilon^2\Delta v+c(x)v=a(x) |u|^{p-1}u &&\text{in } \Omega \newline  u>0, \ v>0 \text{ in } \Omega, &\text{ and }\quad\frac{\partialu}{\partial\nu} = 0 = \frac{\partial v}{\partial\nu} &&\text{on }\partial\Omega  \end{aligned}  \right.  \end{equation} where $\Omega$ is a smooth bounded domain in $R^n, n\geq 3$.The coefficients $a(x), b(x)$ and $c(x)$ are positive bounded smooth functions.We shall study the existence of point concentrating solutions and discuss therole of the coefficients to determine the concentration profile of thesolutions. We have also discussed some applications of our main theorem towardsthe existence of solutions concentrating on higher-dimensional orbits.

Concentration results for solutions of a singularly perturbed elliptic system with variable coefficients