Singularly perturbed biharmonic problems with superlinear nonlinearities (Q393500)
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scientific article; zbMATH DE number 6249380
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Singularly perturbed biharmonic problems with superlinear nonlinearities |
scientific article; zbMATH DE number 6249380 |
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Singularly perturbed biharmonic problems with superlinear nonlinearities (English)
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23 January 2014
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existence of solutions
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singularly perturbed problems
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0.94398093
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0.94185936
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0.94040966
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0.93273103
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0.93226147
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0.93137497
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0.9285854
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0.92827356
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0.92785454
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The authors establish sufficient conditions for the existence of solutions for singularly perturbed problems NEWLINE\[NEWLINE\begin{cases} \epsilon^4 \Delta^2 u +V(x)u = f(u) & \text{ in } \mathbb{R}^N, \\ u \in H^2(\mathbb{R}^N). \end{cases} NEWLINE\]NEWLINE There exists a sequence \(\{u_n\}_n\) of solutions corresponding to a sequence \(\{\epsilon_n\}_n\) which tends to zero, and having maximum points converging to a minimum point of the potential \(V(x)\).
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