Sturm S Theorem Sturm
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6 Sturm-Liouville Eigenvalue Problems
people.uncw.edushow that Equation (6.1) can be turned into a differential equation of Sturm-Liouville form: d dx p(x) dy dx +q(x)y = F(x). (6.5) Another way to phrase this is provided in the theorem: Theorem 6.1. Any second order linear operator can be put into the form of the Sturm-Liouville operator (6.2). The proof of this is straight forward, as we shall ...
![arXiv:2201.04500v1 [math.AP] 12 Jan 2022](/cache/no-preview.jpg)
arXiv:2201.04500v1 [math.AP] 12 Jan 2022
arxiv.orgComments on Theorem 1: 1. Existence. From the standard variational argument, we can easily obtain the existence. 2. The kernel of L−,µ. By using the Sturm argument, we can obtain the kerL−,µ= {Qµ}. Here we do not need to assume that the parameter µis small enough. 3. The kernel of L+,µ. This case seems more difficult, First, we ...
Introduction to Sturm-Liouville Theory
ramanujan.math.trinity.eduOrthogonality Sturm-Liouville problems Eigenvalues and eigenfunctions Sturm-Liouville equations A Sturm-Liouville equation is a second order linear differential equation that can be written in the form (p(x)y′)′ +(q(x) +λr(x))y = 0. Such an equation is said to be in Sturm-Liouville form. Here p,q and r are specific functions, and λ is a ...