LAUSR

This work concerns the distributional solutions of a conformally invariant system of \begin{document}$ n^{\rm th} $\end{document} -order elliptic equations on \begin{document}$ \mathbb R^n $\end{document} having exponential type nonlinearity. The system in question is a natural generalization of the constant \begin{document}$ Q $\end{document} -curvature equation on \begin{document}$ \mathbb R^n $\end{document} . Under an \begin{document}$ L^1 $\end{document} -finiteness assumption and some assumptions on the coupling coefficients, an asymptotic estimate for solutions as \begin{document}$ \left|x\right|\to \infty $\end{document} is obtained. Under a growth constraint and further \begin{document}$ L^1 $\end{document} -norm assumptions the method of moving spheres is used to show that, up to an additive polynomial of low degree, each of the unknown functions is a standard bubble with common center and scale parameters.