Sturm-Liouville Problems with Discontinuities at Two Interior Points

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Authors

  • Hongmei Han
     Journal Center, Qufu Normal University, Qufu 273165, Shandong ,CN

DOI:

https://doi.org/10.18311/jims/2018/14940

Keywords:

Discontinuous Sturm-Liouville Problems, Transmission Condition, Eigenparameter-dependent Boundary Condition, Eigenvalues, Eigenfunctions, Green Function, The Asymptotic Formulas of Eigenvalues and Eigen Functions.
Quantum Theory

Abstract

In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator A associated with the problem, prove the operator A is self-adjoint in an appropriate space H, construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.

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Published

2018-01-04

How to Cite

Han, H. (2018). Sturm-Liouville Problems with Discontinuities at Two Interior Points. The Journal of the Indian Mathematical Society, 85(1-2), 70–91. https://doi.org/10.18311/jims/2018/14940

Issue

Volume 85, Issue 1-2, January-June 2018

Section

Articles

License

Copyright (c) 2018 Hongmei Han

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2017-02-03
Accepted 2017-09-06
Published 2018-01-04

 

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