Concentration for a biharmonic Schrödinger equation (Q2363199)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Concentration for a biharmonic Schrödinger equation |
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Concentration for a biharmonic Schrödinger equation (English)
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13 July 2017
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The paper deals with the nonlinear stationary biharmonic Schrödinger equation \[ \begin{cases} \varepsilon^4 \Delta^2u+V(x)u=P(x)f(|u|)u, & x\in \mathbb{R}^N,\\ u(x)\to 0, & \text{as}\;|x|\to\infty, \end{cases} \] where \(\varepsilon\) stands for the Planck constant, and \(V\) and \(P\) are spatial distributions of external potentials. By means of variational methods, the author describes concentration phenomena for the solutions when \(\varepsilon\to0.\)
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nonlinear biharmonic Schrödinger equation
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standing waves
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