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Journal of the London Mathematical Society 1983 s2-27(1):106-120; doi:10.1112/jlms/s2-27.1.106
© 1983 by London Mathematical Society
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© Oxford University Press

Oscillation of Eigenfunctions of Weighted Regular Sturm-Liouville Problems

W. N. Everitt, Man Kam Kwong and A. Zettl

Department of Mathematics, The University of Birmingham P.O. Box 363, Birmingham B15 2TT
Department of Mathematical Sciences, Northern Illinois University DeKalb, Illinois 60115, U.S.A.

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.


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