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Linear Sturm–Liouville problems with general homogeneous linear multi‐point boundary conditions
Author(s) -
Kong Qingkai,
St. George Thomas E.
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500080
Subject(s) - sturm–liouville theory , mathematics , interlacing , eigenfunction , eigenvalues and eigenvectors , mathematical analysis , homogeneous , boundary value problem , boundary (topology) , zero (linguistics) , combinatorics , linguistics , physics , philosophy , quantum mechanics , computer science , operating system
In this paper, we study second order linear Sturm–Liouville problems involving one or two homogeneous linear multi‐point boundary conditions in the most general form. We obtain conditions for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions. Furthermore, we reveal the interlacing relations between the eigenvalues of such Sturm–Liouville problems and those of Sturm–Liouville problems with certain two‐point separated boundary conditions.