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Periodic indefinite Sturm-Liouville problems with one turning point. (English) Zbl 1499.34205

Summary: Multiplicity of eigenvalues of the regular indefinite Sturm-Liouville problem \(-y^{\prime \prime} + qy = \lambda wy\) on \([a, b]\) subject to periodic boundary conditions is discussed. A necessary and sufficient condition for the existence of non-simple real eigenvalues is proved. Eigenfunctions corresponding to non-simple real eigenvalues are obtained. In this article, we discuss the interlacing property in one turning point case with periodic boundary conditions.

MSC:

34B24 Sturm-Liouville theory
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
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