Positive periodic solutions for a class of higher-dimensional state-dependent delay functional differential equations with feedback control. (English) Zbl 1161.34346
Summary: We use Krasnoselskii’s fixed point theorem on cones to study the existence of positive periodic solutions of the following class of higher-dimensional state-dependent delay functional differential equations with feedback control
\[
\begin{cases} \dot x(t)=-A(t)x(t)+f(t,x_ t,x(t-\tau(t,x(t))),u(t-\alpha(t))),\\ \dot u(t)=-B(t)u(t)+C(t)x(h(t,x(t))).\end{cases}
\]
In addition, we illustrate our results by applying them to a population model.
References:
| [1] | Huo, H. F.; Li, W. T., Positive periodic solutions of a class of delay differential system with fedback control, Applied Mathematics and Computation, 148, 35-46 (2004) · Zbl 1057.34093 |
| [2] | Krasnosel’skii, M. A., Positive solutions of operator equation (1964), Noodhoff: Noodhoff Groningen · Zbl 0121.10604 |
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