On the existence of infinitely many critical points of the functional \(\int_{\Omega}f(x,u,Du)dx\) (Q795318)
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scientific article; zbMATH DE number 3861883
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of infinitely many critical points of the functional \(\int_{\Omega}f(x,u,Du)dx\) |
scientific article; zbMATH DE number 3861883 |
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On the existence of infinitely many critical points of the functional \(\int_{\Omega}f(x,u,Du)dx\) (English)
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1982
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The authors prove that, if the functional \(F(u)=\int_{\Omega}f(x,u,Du)dx\) is even on \(H^ 1_ 0(\Omega)\) and satisfies some growth conditions, then there exist infinitely many critical points. This result generalizes a theorem of \textit{A. Ambrosetti}, \textit{P. H. Rabinowitz} [J. Funct. Anal. 14, 349-381 (1973; Zbl 0273.49063)] on the functional \(G(u)=\int_{\Omega}{1\over2}| Du|^ 2+g(u)dx\).
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multiple integrals
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nonlinear Dirichlet problem
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