Some eigenvalue problems for vectorial Sturm-Liouville equations with eigenparameter dependent boundary conditions

Author:
Chi-Hua Chan

Journal:
Trans. Amer. Math. Soc. **364** (2012), 119-136

MSC (2010):
Primary 34B08

DOI:
https://doi.org/10.1090/S0002-9947-2011-05269-4

Published electronically:
August 9, 2011

MathSciNet review:
2833579

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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the -dimensional vectorial Sturm-Liouville equation

For the case , we show that the *algebraic multiplicity* of an eigenvalue of the problem as a zero of the *characteristic function*

*geometric multiplicity*. By the theory of Hadamard's factorization, we also prove that the

*characteristic function*is uniquely determined by the

*spectral set*of the equation. Moreover, we consider the inverse problem for the equation, i.e., how many

*spectral sets*can determine the potential function uniquely, and we find that three

*spectral sets*are necessary for us to determine the potential function uniquely.

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Additional Information

**Chi-Hua Chan**

Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China

Email:
d917201@oz.nthu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9947-2011-05269-4

Received by editor(s):
August 27, 2009

Received by editor(s) in revised form:
December 8, 2009

Published electronically:
August 9, 2011

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.