ON THE ONE‐DIMENSIONAL SCHRÖDINGER EQUATION WITH A QUASI‐PERIODIC POTENTIAL
ON THE ONE‐DIMENSIONAL SCHRÖDINGER EQUATION WITH A QUASI‐PERIODIC POTENTIAL
复制标题
DOI：
10.1111/j.1749-6632.1980.tb29679.x
复制
发表时间：
1980-12
影响因子：
5.2
通讯作者：
H. Rüssmann
中科院分区：
文献类型：
--
作者：
H. Rüssmann
WLR…w是一组给定的频率和傅里叶系数ck。k, = ck，满足8，c,12 -；r，问题是，对于E的什么值方程1有两个线性无关的拟周期解？这个问题最早是由Dinaburg和Sinai在2010年的案例中解决的。他们证明了，在附加的假设(A)下，频率w . . . .不满足不等式
where wlr . . . w, is a given set of frequencies and the Fourier coefficients, c k , , . k, = ck, satisfy 8, I c,12 -; r. The question is, For what values of E does equation 1 have two linearly independent quasi-periodic solutions? This problem was first treated in the case where n > 1 by Dinaburg and Sinai.' They proved that, under the additional assumptions that ( A , ) the frequencies w , . . . . on satisfy the inequalities