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Linear Sturm‐Liouville problems with multi‐point boundary conditions
Author(s) -
Kong Lingju,
Kong Qingkai,
Kwong Man K.,
Wong James S. W.
Publication year - 2013
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.201200187
Subject(s) - sturm–liouville theory , mathematics , interlacing , eigenvalues and eigenvectors , eigenfunction , boundary value problem , mathematical analysis , boundary (topology) , robin boundary condition , zero (linguistics) , mixed boundary condition , simple (philosophy) , nonlinear system , linguistics , physics , philosophy , epistemology , quantum mechanics , computer science , operating system
We study second order linear Sturm‐Liouville problems which involve one or two multi‐point boundary conditions. Conditions for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions are derived. We also show that these eigenvalues are algebraically simple. Moreover, we obtain certain interlacing relations between the eigenvalues of Sturm‐Liouville problems with multi‐point boundary conditions and those with two‐point separated boundary conditions. The work for multi‐point Sturm‐Liouville problems will set up a foundation for the further studies of nonlinear boundary value problems with multi‐point boundary conditions.