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
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
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