Indefinite Sturm–Liouville problems
Indefinite Sturm–Liouville problems
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DOI：
10.1017/s0308210500002584
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发表时间：
2003-06
期刊：
影响因子：
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通讯作者：
Qingkai Kong;Hongyou Wu;A. Zettl;M. Möller
中科院分区：
文献类型：
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作者：
Qingkai Kong;Hongyou Wu;A. Zettl;M. Möller
研究了具有实系数和权函数的正则和奇异Sturm-Liouville问题的谱。自伴边界条件可以是正则的或奇异的，也可以是分离的或耦合的。充分条件被发现（i）的频谱是真实的和无界以下以及以上和（ii）的本质谱是空的。还发现是一个上限的非实特征值的数量。这些结果是通过研究不确定性问题（具有改变符号的权函数）和相应的确定性问题之间的相互作用来实现的。我们的方法在很大程度上依赖于Krein空间的算子理论。
We study the spectrum of regular and singular Sturm–Liouville problems with real-valued coefficients and a weight function that changes sign. The self-adjoint boundary conditions may be regular or singular, separated or coupled. Sufficient conditions are found for (i) the spectrum to be real and unbounded below as well as above and (ii) the essential spectrum to be empty. Also found is an upper bound for the number of non-real eigenvalues. These results are achieved by studying the interplay between the indefinite problems (with weight function which changes sign) and the corresponding definite problems. Our approach relies heavily on operator theory of Krein space.