Analysis of Sturm-Liouville Eigenproblem with Interior Singularities and a Perturbation Parameter | Zendy

Thomas M. Acho | Zendy

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Analysis of Sturm-Liouville Eigenproblem with Interior Singularities and a Perturbation Parameter

Author(s) -

Thomas M. Acho

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/914527

Subject(s) - eigenfunction , sturm–liouville theory , gravitational singularity , eigenvalues and eigenvectors , boundary value problem , mathematics , mathematical analysis , perturbation (astronomy) , interval (graph theory) , boundary (topology) , turning point , pure mathematics , physics , combinatorics , quantum mechanics , acoustics , period (music)

We devote this work to the discussion underpinning the derivation of eigenvalues and eigenfunction solutions for Sturm-Liouville boundary value problems. The study reveals that the parameter dependent nonstandard Sturm-Liouville boundary value problem with interior singularities may have more than two turning points. The Titchmarsh-Weyl m-function theory is applied here to obtain eigenfunction solutions valid for the whole interval in which pole singularities and two turning points are present. For the first time, with minimal constraints, the validity of the eigenfunction solutions are discussed when there are more than two turning points present. The eigenvalues are subsequently derived

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