ABSTRACT
In this section, a perturbation of the Sturm-Liouville operator by a Volterra integral operator is considered. The presence of an ”aftereffect” in a mathematical model produced qualitative changes in the study of the IP. The main results of the section are expressed by Theorems 13.1-13.3. Note that the IP for integro-differential oper ators in various formulations has been studied in [119]—[122]. Among other things, a connection is pointed out in [120] between the IP under consideration here and the completeness of the eigen-and associated functions of a bundle of fourth-order integrodifferential operators.
