Nonlinear Schrödinger Equations with Steep Magnetic Well
Nonlinear Schrödinger Equations with Steep Magnetic Well
复制标题
具有陡磁阱的非线性薛定谔方程
DOI：
10.3836/tjm/1374497510
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S. Shirai
中科院分区：
文献类型：
--
作者：
S. Shirai
。研究了RN上的非线性磁薛定谔方程−(∇−iλA)2 u=f(x，|u|2)u，其中N≥2是超线性的亚临界非线性项。假设矢势A和相关的磁场fi在公共有界开集Ω上为零。结果表明，上述方程有越来越多的解，这些解在Ω附近局部化为λ→∞。
. We study the nonlinear magnetic Schrödinger equation, − ( ∇ − iλA) 2 u = f(x, | u | 2 )u on R N , where N ≥ 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 Ω . It is shown that the equation above has more and more solutions which are localized near Ω as λ → ∞ .