Dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition

In this paper, we discuss the continuous dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition by using of implicit function theorem. A geometric structure on SL(2,R) containing real coupled boundary conditions is firstly clarified, that is, the smooth embeddin...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 538; no. 2; p. 128398
Main Author:	Yang, Xinya
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.10.2024
Subjects:	Differential Implicit function theorem Real coupled boundary condition Smooth manifold Implicit function theorem Real coupled boundary condition Smooth manifold Differential
ISSN:	0022-247X, 1096-0813
Online Access:	Get full text
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Summary:	In this paper, we discuss the continuous dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition by using of implicit function theorem. A geometric structure on SL(2,R) containing real coupled boundary conditions is firstly clarified, that is, the smooth embedding submanifold. Under this structure, we verify the continuous differentiability of the n-th eigenvalue with regard to the boundary condition and explicitly present the expression for its differential. Moreover, a sufficient condition for recognizing double eigenvalues is given.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2024.128398