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Completeness and nodes of eigenfunctions for a class of unconventional Sturm-Liouville eigenvalue problem

Qiong-Gui Lin

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Abstract

The vibration of a string or a rod with their ends connected to particles(concentrated mass),orsimilar problems,result in a class of unconventional Sturm-Liouville eigenvalue problem after separation of variables.The completeness of the eigenfunctions of such eigenvalue problems is proved.It is also proved that the n-th eigenfunction has n-1 nodes(zeros).

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What this paper is about

The vibration of a string or a rod with their ends connected to particles(concentrated mass),orsimilar problems,result in a class of unconventional Sturm-Liouville eigenvalue problem after separation of variables.The completeness of the eigenfunctions of such eigenvalue problems is proved.It is also proved that the n-th eigenfunction has n-1 nodes(zeros).

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Available abstract

The vibration of a string or a rod with their ends connected to particles(concentrated mass),orsimilar problems,result in a class of unconventional Sturm-Liouville eigenvalue problem after separation of variables.The completeness of the eigenfunctions of such eigenvalue problems is proved.It is also proved that the n-th eigenfunction has n-1 nodes(zeros).

Key concepts: Eigenfunction, Sturm–Liouville theory, Eigenvalues and eigenvectors, Completeness (order theory), Physics, String (physics), Separation of variables, Class (philosophy)

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