Linear Sturm-Liouville problems with multi-point boundary conditions (Q2852451)

For the Sturm-Liouville problem NEWLINE\[NEWLINE-y''=\lambda wyNEWLINE\]NEWLINE on a finite interval \((a,b)\), with \(0<w\in C^1[a,b]\), and with one or both of the boundary conditions of multi-point type, the authors derive sufficient conditions for the existence of a sequence of positive eigenvalues, with consecutive zero counts of the eigenfunctions. They show that these eigenvalues are algebraically simple, and they obtain interlacing relations between the eigenvalues of this problem and those for the corresponding problem with classical two-point separated boundary conditions. They discuss the relevance of their results for the nonlinear problem NEWLINE\[NEWLINE-y''=wf(y)NEWLINE\]NEWLINE with similar multi-point boundary conditions, and also compare them with recent results of \textit{F. Genoud} and \textit{B. P. Rynne} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 18, 7269--7284 (2011; Zbl 1235.34051)].