On a semilinear Robin problem involving critical Sobolev exponent (Q2770155)
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scientific article; zbMATH DE number 1702870
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a semilinear Robin problem involving critical Sobolev exponent |
scientific article; zbMATH DE number 1702870 |
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On a semilinear Robin problem involving critical Sobolev exponent (English)
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19 September 2002
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critical Sobolev exponent
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positive solutions
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semilinear elliptic equations
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Yamabe problem
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The authors consider the problem NEWLINE\[NEWLINE-\Delta u = Q(x) u^{2^*-1}, \quad u>0 \quad\text{in }\Omega,\qquad \frac{\partial u}{\partial\nu} + a(x) u = 0 \quad \text{on } \partial\Omega,NEWLINE\]NEWLINE with smooth bounded \(\Omega\subset\mathbb R^N\), \(N\geq 3\), \(2^*=\frac{2N}{N-2}\). The effect of the level sets topology of \(Q(x)\) on the solvability is studied.
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