A note on a nonlinear functional differential system with feedback control

Yuqing Wang, College of Science, Minzu University of China, Beijing, P. R. China
Xiaoming He, College of Science, Minzu University of China, Beijing, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 13. (2009), pp. 1-9.

Abstract: In this note we apply Avery-Peterson multiple fixed point theorem to investigate the existence of multiple positive periodic solutions to the following nonlinear non-autonomous functional differential system with feedback control
\[\left\{\begin{array}{l}
\frac{dx}{dt}=-r(t)x(t)+F(t,x_t,u(t-\delta(t))),\\
\frac{du}{dt}=-h(t)u(t)+g(t)x(t-\sigma(t)).\\
\end{array}\right.\]
We prove the system above admits at least three positive periodic solutions under certain growth conditions imposed on $F$.

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