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June 2013 Nonlinear Schrödinger Equations with Steep Magnetic Well
Shin-ichi SHIRAI
Tokyo J. Math. 36(1): 1-23 (June 2013). DOI: 10.3836/tjm/1374497510

Abstract

We study the nonlinear magnetic Schrödinger equation, $-(\nabla -i\lambda A)^{2}u=f(x,|u|^{2})u$ on $\mathbb{R}^{N}$, where $N \geq 2$ and the nonlinearity is super-linear and subcritical. The vector potential $A$ and the associated magnetic field are assumed to vanish on a common bounded open set $\Omega$. It is shown that the equation above has more and more solutions which are localized near $\Omega$ as $\lambda \to \infty$.

Citation

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Shin-ichi SHIRAI. "Nonlinear Schrödinger Equations with Steep Magnetic Well." Tokyo J. Math. 36 (1) 1 - 23, June 2013. https://doi.org/10.3836/tjm/1374497510

Information

Published: June 2013
First available in Project Euclid: 22 July 2013

zbMATH: 1288.35034
MathSciNet: MR3112374
Digital Object Identifier: 10.3836/tjm/1374497510

Subjects:
Primary: 35J60
Secondary: 35B20, 35J10

Rights: Copyright © 2013 Publication Committee for the Tokyo Journal of Mathematics

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Vol.36 • No. 1 • June 2013
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