Abstract
AbstractAs early as 1910, Weyl gave a classification of the singular Sturm–Liouville equation, and divided it into the Limit Point Case and the Limit Circle Case at infinity. This led to the study of singular Sturm–Liouville spectrum theory. With the development of applications, the importance of singular Sturm–Liouville problems with a weighted function becomes more and more significant. This paper focuses on the study of singular Sturm–Liouville problems with a weighted function. Finally, an example of singular Sturm–Liouville problems with a weighted function is given.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference25 articles.
1. Aronsajn, N.: On a problem of Weyl in the theory of singular Sturm–Liouville equations. Am. J. Math. 79, 597–610 (1957)
2. Probability and Its Applications.;R. Carmona,1990
3. Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955)
4. Del Rio, R., Jitomirskaya, S., Last, Y., Simon, B.: Operators with singular continuous spectrum. IV. Hausdorff dimensions, rank one perturbations, and localization. J. Anal. Math. 69, 153–200 (1996)
5. Del Rio, R., Makarov, N., Simon, B.: Operators with singular continuous spectrum. II. Rank one operators. Commun. Math. Phys. 165(1), 59–67 (1994)