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A new method of solving the index problem for Sturm-Liouville eigenvalues

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Abstract

Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of sequences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic principle are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.

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Authors and Affiliations

  1. College of Mathematics science, Inner Mongolia Normal University, Hohhot, 010022, China

    Gui-Xia Wang

  2. Mathematics Department, Inner Mongolia University, Hohhot, 010021, China

    Jiong Sun

Authors
  1. Gui-Xia Wang
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  2. Jiong Sun
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Correspondence to Gui-Xia Wang.

Additional information

Supported by the National Natural Science Foundation of China (No. 11361039 and 11161030), the Natural Science Foundation of Inner Mongolia Province, China (No. 2013MS0116).

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Wang, GX., Sun, J. A new method of solving the index problem for Sturm-Liouville eigenvalues. Acta Math. Appl. Sin. Engl. Ser. 31, 1001–1012 (2015). https://doi.org/10.1007/s10255-015-0520-2

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  • DOI: https://doi.org/10.1007/s10255-015-0520-2

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