Oscillation property of the spectrum of multipoint boundary value problems (Q1589037)

The author studies the eigenvalue problem for equations \[ Ly \equiv y^{(n)}+\sum_{k=0}^{n-1} p_{k}(\cdot)y^{(k)}=\lambda q(\cdot)y \] under the conditions \[ l_j y \equiv \sum_{k=1}^n b_{jk}y^{(n-k)} (c_j) = 0, \quad j=1,\dots,r, \] \[ y^{(\nu_i)}(a_i) = 0, \quad \nu_i = 0,\dots,k_i-1, \quad i=1,\dots,m, \] with \(1<r<n\), \(k_1+\cdots+k_m = n-r\), \(a \leq c_1 \leq\cdots \leq c_r \leq b\), \(a\leq a_1 \leq\cdots\leq a_m \leq b\). Under some conditions on the data of the considered problem, an oscillation property of the spectrum is proved. The obtained result generalizes the author's earlier results to the more general case of multipoint boundary value problems.