Existence of sign changing solutions for some critical problems on \(\mathbb R^N\) (Q1779034)
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scientific article; zbMATH DE number 2177445
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of sign changing solutions for some critical problems on \(\mathbb R^N\) |
scientific article; zbMATH DE number 2177445 |
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Existence of sign changing solutions for some critical problems on \(\mathbb R^N\) (English)
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21 June 2005
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The paper deals with constructing families of positive and changing-sign solutions for both the slightly subcritical and slightly supercritical equations \[ -\Delta u + V(x)u=N(N-2)| u| ^{\frac{4}{N-2}\pm\epsilon} u\qquad \text{ in}\;{\mathbb R}^N, \] which blow-up and concentrate at different points of \({\mathbb R}^N\) as \(\epsilon\) goes to 0, under certain conditions on the potential \(V.\)
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Critical Sobolev exponent
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blowing-up solution
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sign changing solutions
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