Generalized multipoint conjugate eigenvalue problems (Q1591043)

The authors study the following boundary value problem \[ y^{(n)}=\lambda P(t,y),\quad t\in(0,1), \qquad y^{(j)}(t_i)=0,\quad j=0,1,\dots,n_i-1,\;i=1,\dots,r, \] with \(r\geq 2, n_i\geq 1\) for \(i=1,\dots,r\), \(\sum^r_{i=1}n_i=n\) and \(0=t_1<t_2<\dots<t_r+1\). They determine those positive values of \(\lambda\) for which the boundary value problem has a solution that is ``positive'' in some sense. Specifically, criteria are developed for \(\lambda\) to constitute an interval, bounded as well as unbounded, and more such explicit intervals for \(\lambda\) are presented. The authors include examples to illustrate the importance of the results obtained.