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Oscillation of Eigenfunctions of Weighted Regular Sturm‐Liouville Problems
Author(s) -
Everitt W. N.,
Kwong Man Kam,
Zettl A.
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-27.1.106
Subject(s) - eigenfunction , sturm–liouville theory , mathematics , oscillation (cell signaling) , interval (graph theory) , mathematical analysis , zero (linguistics) , measure (data warehouse) , boundary value problem , eigenvalues and eigenvectors , oscillation theory , set (abstract data type) , value (mathematics) , pure mathematics , combinatorics , physics , differential equation , quantum mechanics , statistics , ordinary differential equation , linguistics , philosophy , database , biology , computer science , programming language , genetics , collocation method
We investigate the zeros of eigenfunctions of regular Sturm–Liouville boundary value problems with general weight functions w . In particular we are interested in the case when the set of zeros of w has positive measure. We find that in this case the first eigenfunction may have one or more zeros in the interval, in contrast to the classical case when w is positive. Necessary and sufficient conditions on w and the other coefficients are found such that the first eigenfunction has no zero.