Global solutions of nonlinear Schrödinger equations
Global solutions of nonlinear Schrödinger equations
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DOI：
10.1007/s00526-017-1145-5
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发表时间：
2017-03
影响因子：
2.1
通讯作者：
M. Schechter
中科院分区：
文献类型：
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作者：
M. Schechter
我们研究非线性薛定谔方程，但不对势或非线性项做出任何周期性假设。这阻止我们使用浓度紧致方法。我们的假设是势不会改变线性算子的基本谱。这导致成为频谱的绝对连续部分。如果存在无限多个负特征值，它们将收敛于 0。在每种情况下，我们都会获得非平凡解。我们还获得了最少能量的解决方案。
We study the nonlinear Schrödinger equation inwithout making any periodicity assumptions on the potential or on the nonlinear term. This prevents us from using concentration compactness methods. Our assumptions are such that the potential does not change the essential spectrum of the linear operator. This results inbeing the absolutely continuous part of the spectrum. If there are an infinite number of negative eigenvalues, they will converge to 0. In each case we obtain nontrivial solutions. We also obtain least energy solutions.