Tokyo Journal of Mathematics

Nonlinear Schrödinger Equations with Steep Magnetic Well

Shin-ichi SHIRAI

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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 $\lambda \to \infty$.

Article information

Source
Tokyo J. Math., Volume 36, Number 1 (2013), 1-23.

Dates
First available in Project Euclid: 22 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1374497510

Digital Object Identifier
doi:10.3836/tjm/1374497510

Mathematical Reviews number (MathSciNet)
MR3112374

Zentralblatt MATH identifier
1288.35034

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B20: Perturbations 35J10: Schrödinger operator [See also 35Pxx]

Citation

SHIRAI, Shin-ichi. Nonlinear Schrödinger Equations with Steep Magnetic Well. Tokyo J. Math. 36 (2013), no. 1, 1--23. doi:10.3836/tjm/1374497510. https://projecteuclid.org/euclid.tjm/1374497510


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