On the nonself-adjoint ordinary differential operators with periodic boundary conditions
Asymptotic formulae are proved for the eigenvalues and eigenfunctions of the operators generated in \(L_{2} [0,1]\) by a differential expression of the form \[ l_{m} (y) = y^{(m)} + p_{2} (x) y^{(m - 2)} + p_{3} (x) y^{(m - 3)} + \cdots+ p_{m} (x) y \] with periodic \(y^{(k)} (1) = y^{(k)}(0)\) \((k = 0,1,\dots,m - 1)\) and also with anti-periodic boundary conditions. The problem of the completeness of the corresponding root functions is also considered.
scientific article; zbMATH DE number 5728346