On monotone solutions and a self-adjoint spectral problem for a functional-differential equation of even order - Manuel Alves; Sergey Labovskiy (Electronic Journal of Qualitative Theory of Differential Equations, 2019)
For a self-adjoint boundary value problem for a functional-differential equation of even order, the basis property of the system of eigenfunctions and the equivalence of such statements as the positivity of the corresponding quadratic functional, the Jacobi condition and the positivity of the Green function are established.