Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter
Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter
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谱参数非线性奇异Sturm-Liouville问题的特征值累加
DOI：
10.1006/jdeq.1999.3671
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发表时间：
1999
影响因子：
2.4
通讯作者：
J. Lutgen
中科院分区：
文献类型：
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作者：
J. Lutgen
摘要对于某些奇异Sturm-Liouville方程，其系数连续依赖于区间Λ的谱参数λ，证明了在Λ端点ν处特征值的积累/不积累本质上是由方程在边界λ = ν处的振荡性质决定的。作为应用，得到了径向狄拉克算子和Klein-Gordon方程的新结果。另外三种物理应用也被考虑。
Abstract For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ = ν . As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.