Uniqueness and profile of positive solutions of a critical exponent problem with Hardy potential (Q393035)
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scientific article; zbMATH DE number 6245992
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness and profile of positive solutions of a critical exponent problem with Hardy potential |
scientific article; zbMATH DE number 6245992 |
Statements
Uniqueness and profile of positive solutions of a critical exponent problem with Hardy potential (English)
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15 January 2014
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critical exponent
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Hardy's inequality
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Morse index
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uniqueness
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asymptotic behavior
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The authors obtain uniqueness and blow-up profile of the positive least energy solution to a critical exponent problem with Hardy potential NEWLINE\[NEWLINE \begin{cases} \Delta u+{\mu\over{|x|^2}}u+f(u)=0 & \text{in}\;\Omega,\\ u=0 & \text{on}\;\partial\Omega, \end{cases} NEWLINE\]NEWLINE where \(f\) is a superlinear function, \(\Omega\subset{\mathbb R}^N\) is a bounded and smooth domain and \(0\leq\mu<{{(N-2)^2}\over4}.\)
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