On a periodic Schrödinger equation with nonlocal superlinear part
On a periodic Schrödinger equation with nonlocal superlinear part
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DOI：
10.1007/s00209-004-0663-y
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发表时间：
2004-04
影响因子：
0.8
通讯作者：
Nils Ackermann
中科院分区：
文献类型：
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作者：
Nils Ackermann
我们考虑Choquard-Pekar方程 并重点讨论了周期电位V的情况。对于一大类偶函数W，我们证明了解的存在性和多重性。本质上，条件是0不在线性部分-Δ+ V的谱中，并且W不改变符号。我们的结果推广到更一般的非线性项在任意空间维数N ≥2。
We consider the Choquard-Pekar equation and focus on the case of periodic potentialV. For a large class of even functionsWwe show existence and multiplicity of solutions. Essentially the conditions are that 0 is not in the spectrum of the linear part −Δ+Vand thatWdoes not change sign. Our results carry over to more general nonlinear terms in arbitrary space dimensionN≥2.