Spectral properties of a Sturm–Liouville type differential operator with a retarding argument

Spectral properties of a differential operator of Sturm–Liouville type are studied in the case of retarding argument with different boundary conditions. The asymptotics of solutions to the correspoding differential equation is studied in the case of summable potential. An asymptotics of eigenvalues and an asymptotics of eigenfunctions of the differential operator is calculated in each considered case.