Uniform repellers for processes with applications to periodic differential systems (Q1813822)

The differential equation (1) \(x'= f(t,x)\), \(f: \mathbb{R}\times \Omega\to \mathbb{R}^ p\), \(\Omega\) open in \(\mathbb{R}^ p\), is persistent for a closed set \(M\subseteq \Omega\) if \(\text{int } M\) is invariant for (1) and if there is an \(\eta>0\) such that \(\liminf_{t\to+\infty} d(x(t),b dy M)> \eta\) for every solution \(x(t)\) of (1) satisfying \(x(0)\in \text{int }M\). The author establishes sufficient conditions for uniform persistence when (1) is nonautonomous. These results generalize earlier results for autonomous differential equations [\textit{J. Hofbauer}, Monatsh. Math. 91, No. 3, 233-240 (1981; Zbl 0449.34039)] and for semidynamical systems [\textit{A. Fonda}, Proc. Am. Math. Soc. 104, No. 1, 111-116 (1988; Zbl 0667.34065)].