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Positive periodic solutions of a class of functional differential systems with feedback controls. (English) Zbl 1064.34049

The paper is concerned with the infinite delay functional-differential system with a parameter and feedback controls \[ \left\{ \begin{aligned} \dot x(t)& =A(t)x(t)-\lambda F(t,x_t,x(g(t,x(t))), u(\alpha(t,x(t)))), \\ \dot u(t)& =-B(t)u(t)+E(t,x_t,x(h(t,x(t)))), \end{aligned} \right. \] where \(A(t), B(t)\) are periodic diagonal \(n\times n\)-matrices. Under some assumptions, the existence and nonexistence of positive periodic solutions are shown.

MSC:

34K13 Periodic solutions to functional-differential equations
34K35 Control problems for functional-differential equations
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References:

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