Compactness and the Palais-Smale property for critical Kirchhoff equations in closed manifolds (Q901317)
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scientific article; zbMATH DE number 6528207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compactness and the Palais-Smale property for critical Kirchhoff equations in closed manifolds |
scientific article; zbMATH DE number 6528207 |
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Compactness and the Palais-Smale property for critical Kirchhoff equations in closed manifolds (English)
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11 January 2016
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In this article, both the Palais-Smale property and the compactness of solutions for critical Kirchhoff equations is proved. This is achieved by the usage of energy arguments. The author treats the case where absolutely no sign assumption is made upon the solutions. Additionally, he proves the existence of a mountain-pass solution to the equation. Further, its ground-states structure is discussed as well as the uniqueness of this solution in extreme cases.
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compactness
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ground-states
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Kirchhoff equation
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mountain-pass solution
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Palais-Smale property
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