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In this paper, we study the asymptotic behavior of solutions to the semilinear elliptic problem involving critical Sobolev exponent with lower order perturbation, which was considered by Han and Rey before. We focus our attention on the least energy solutions obtained by the method of Brezis and Nirenberg, and show that the blow up point of the least energy solutions is a minimum point of the (positive) Robin function on the domain. This additional characterization extends the former result of Han and Rey in this case.

On the Location of Blow up Points of Least Energy Solutions to the Brezis-Nirenberg Equation