| Abstract: |
| We consider an elliptic equation involving the Hardy-Sobolev critical exponent.
Concerning this problem, position of the singularity on the bounded domain plays a crucial role.
We study existence and nonexistence of least-energy solution and effect of the mean curvature at the singularity.
In order to prove existence and nonexistence, we investigate asymptotic behavior of least-energy solution.
By investigating asymptotic behavior, we can find the scale of the domain also plays an important role on existence and nonexistence in addition to the mean curvature. |
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