### On discreteness of spectrum of a functional differential operator

We study conditions of discreteness of spectrum of the functional-differential operator $$\mathcal{L}u=-{u}^{\text{'}\text{'}}+p\left(x\right)u\left(x\right)+{\int}_{-\infty}^{\infty}(u\left(x\right)-u\left(s\right)){\mathrm{d}}_{s}r(x,s)$$ on $(-\infty ,\infty )$. In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.