Multiple positive periodic solutions of nonlinear functional differential system with feedback control. (Q1419752)

The paper deals with a two-dimensional nonautonomous system of functional-differential equations of a special form. Namely, it is assumed that each equation consists of the main part (linear in the state variable) and the feedback control that is a nonlinear function containing the delayed links. The basic results of the work are the theorems 1 and 2 giving sufficient conditions for the existence of at least two positive \(\omega\)-periodic solutions of the considered system. The proofs of the theorems are based on a generalization of the well-known fixed-point theorem of Leggett-Williams.