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Asymptotic behavior of a differential operator with discontinuities at two points

โœ Scribed by Qiuxia Yang; Wanyi Wang

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
179 KB
Volume
34
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

In this paper, we study a Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. By establishing a new operator A associated with the problem, we prove that the operator A is self-adjoint in an appropriate space H, discuss completeness of its eigenfunctions in H, and obtain its Green function.

๐Ÿ“œ SIMILAR VOLUMES

The Spectral Theory of Second Order Two-
The Spectral Theory of Second Order Two-Point Differential Operators II. Asymptotic Expansions and the Characteristic Determinant
โœ J. Locker ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 443 KB

In this second paper of a four-part series, we construct the characteristic determinant of a two-point differential operator \(L\) in \(L^{2}[0,1]\), where \(L\) is determined by \(\ell=-D^{2}+q\) and by independent boundary values \(B_{1}, B_{2}\). For the solutions \(u(\cdot ; \rho)\) and \(v(\cdo