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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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 538; H. 2; S. 128398
1. Verfasser: Yang, Xinya
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.10.2024
Schlagworte:
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
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Zusammenfassung: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