Аннотация:Abstract. The singular Sturm–Liouville boundary value problem for the equation
−(pu ′ ) ′ + p 1 u +
∫
l
0
u(s)d s r(x,s) = 0
under certain symmetry condition is considered. It is established completeness of sys-
tem of eigenfunctions of the corresponding eigenvalue problem, equivalence of a number
of statements such as positivity of Green’s function, positive definiteness of a quadratic
functional, and others assertions.