Concentration for a biharmonic Schrödinger equation
type: Item
instance of: scholarly article
title: Concentration for a biharmonic Schrödinger equation
zbMATH Open document ID: 1373.35107
author: Yanyan Li
published in: Pacific Journal of Mathematics
publication date: 2017-07-13T00:00:00Z
review text: 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 \(\varepsilon\to0.\)
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 31B30
Mathematics Subject Classification ID: 35J35
zbMATH DE Number: 6744687
zbMATH Keywords: nonlinear biharmonic Schrödinger equation
zbMATH Keywords: standing waves
MaRDI profile type: Publication
full work available at URL: pjm.2017.289.469
OpenAlex ID: W2725551267
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DOI: 10.2140/PJM.2017.289.469
description: scientific article