Basis property of chains of eigenfunctions for certain boundary-value problems (Q5951108)

The author studies completeness properties of the eigenfunctions of the ordinary differential equation system \[ l(y,\lambda)= \lambda^{n-1}l_1(y)+\cdots+ l_n(y)= 0, \] \[ U_j(y, \lambda)= \sum^{n-1}_{k=0} a_{jk}(\lambda) y^{(k)}(0)+ b_{jk}(\lambda) y^k(1)= 0,\quad j= 1,\dots, n, \] where \[ l_s(y)= \sum^s_{v=0} P_{vs}(x) y^{(v)},\quad P_{ss}= \text{const},\quad P_{nn}\neq 0, \] the \(a_{jk}(\lambda)\), \(b_{jk}(\lambda)\) are arbitrary polynomials in \(\lambda\), and \(\lambda\) is the spectral parameter.