Positive radially symmetric ground states to a bi-harmonic problem. (Q2093362)
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scientific article; zbMATH DE number 7613046
| Language | Label | Description | Also known as |
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| English | Positive radially symmetric ground states to a bi-harmonic problem. |
scientific article; zbMATH DE number 7613046 |
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Positive radially symmetric ground states to a bi-harmonic problem. (English)
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7 November 2022
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The author considers the existence of positive solutions to the semilinear problem for the bi-harmonic operator \[ (-\Delta)^2u+u=|u|^{p-1}u \] in \(\mathbb{R}^n\). One of the main tools is an interesting generalization of the Strauss-Ni Lemma for radially symmetric functions in higher order Sobolev spaces.
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semilinear problem for the bi-harmonic operator
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Schwarz symmetrization method
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generalized Strauss-Ni Lemma
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Sobolev spaces
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