The Leray-Schauder boundary condition in critical point theory (Q923982)
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scientific article; zbMATH DE number 5586853
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Leray-Schauder boundary condition in critical point theory |
scientific article; zbMATH DE number 5586853 |
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The Leray-Schauder boundary condition in critical point theory (English)
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24 July 2009
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The author presents a version of Schechter's bounded mountain pass theorem in a Hilbert space not identified to its dual. An application to positive solutions of elliptic boundary value problems \[ \begin{cases} \Delta u+f(u)=0 & \text{in}\;\Omega,\\ u>0\;\text{in}\;\Omega, & u=0\;\text{on}\;\partial\Omega, \end{cases} \] is given.
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critical point
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mountain pass lemma
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Leray-Schauder condition
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positive solution
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elliptic problem
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