We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a rotationally symmetric Fowler type solution. This result generalizes the celebrated work due to Caffarelli, Gidas and Spruck  who studied asymptotic proprieties to the classic Yamabe equation. In addition, we generalize similar results by Marques  for inhomogeneous context, that is, when the metric is not necessarily conformally flat.
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Almir Silva Santos, Rayssa Caju, João Marcos do Ó, Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 6, pp. 1575–1601DOI 10.1016/J.ANIHPC.2019.02.001