Abstract:
Necessary and sufficient conditions for discreteness of spectrum for the singular second order functional differential operator of the form
$$
\frac{1}{\rho(x)}\left(-(p(x)u')'+q(x)u-\int_a^b u(s)r(x,ds)\right),
\; x\in (a,b),\; -\infty\le a<b\le\infty
$$
are obtained.
Keywords:discreteness of spectrum, functional differential operator.