Eigenvalue theorems for discrete multipoint conjugate boundary value problems (Q1963892)

Consider the boundary value problem \[ \begin{aligned} & \Delta^n y(k)= \lambda P(k,y, \Delta y,\dots,\Delta^{n-1}y),\;k=0,\dots,m,\\ & \Delta^j y(k_i) =0,\;j=0, \dots, n_i-1,\;i=0,1, \dots,r,\\ & \text{where }r\geq 2,\;n_i\geq 1 \text{ for }i=1,2, \dots,r,\;\sum^r_{i=1} n_i=n \text{ and}\\ & 0=k_i<k_i+n_1 <k_2+n_2< \cdots< k_r\leq k_r+ n_r-1=m+n. \end{aligned} \] The authors characterize the values of \(\lambda\) so that the boundary value problem has a positive solution. Also they obtain criteria for values of \(\lambda\) to form a bounded/unbounded interval. Examples are included in the text for illustration.