Multi-bump bound states for a nonlinear Schrödinger system with electromagnetic fields
Multi-bump bound states for a nonlinear Schrödinger system with electromagnetic fields
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DOI：
10.1016/j.jmaa.2013.03.012
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发表时间：
2013-08
影响因子：
1.3
通讯作者：
Shengmao Fu;Y. Jiao;Z. Tang
中科院分区：
文献类型：
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作者：
Shengmao Fu;Y. Jiao;Z. Tang
本文讨论了具有足够大的λ的具有电磁场的非线性薛定谔系统，其中I是虚单位，α>；1，β>；1，α+β<；Θ，Θ=2NN−2，N≥3，Θ=+∞，N=1，2。A(X)和B(X)是实值电磁矢势。V(X)和W(X)是RN上的实值连续非负函数。通过修正非线性和使用衰减流，我们证明了如果Ω：=INT−1(0)∩INT W−1(0)有几个孤立连通分支Ω1，Ω2，…，Ω使得Ωi的内部不为空，且∂Ωi对所有i∈{1，2，…都是光滑的，k}，则对任意非空子集J⊂{1，2，…，k}存在(Sλ)的(uλ，vλ)解λ>；0 Large.此外，对于任何序列λn→∞，直到一个子序列[公式：见文本]在Ωj(j∈J)中收敛到下列极限问题的最小能量解，并且在⋃j∈JΩjto(0，0)之外。
In this paper, we are concerned with the following nonlinear Schrödinger system with electromagnetic fields for sufficiently large λ, where i is the imaginary unit, α>1,β>1,α+β<Θ and Θ=2NN−2 for N≥3,Θ=+∞ for N=1,2. A(x) and B(x) are real-valued electromagnetic vector potentials. V(x) and W(x) are real-valued continuous nonnegative functions on RN. By modifying the nonlinearity and using the decay flow we show that if Ω:=int V−1(0)∩int W−1(0) has several isolated connected components Ω1,Ω2,…,Ωksuch that the interior of Ωiis not empty and ∂Ωiis smooth for all i∈{1,2,…,k}, then for any non-empty subset J⊂{1,2,…,k} there exists a solution (uλ,vλ) of (Sλ) for λ>0 large. Moreover for any sequence λn→∞, up to a subsequence [Formula: see text] converges in Ωj(j∈J) to a least energy solution of the following limit problem and outside of ⋃j∈JΩjto (0,0).