4 problems

Let $f\in C^3(\mathbb R)$ satisfy the hypotheses $(\mathbf H)$: $xf(x)<0$ for $x\ne0$ with $f'(0)<0$; $f$ has at most one critical point $x^*$, with $f(x)>C$ for some…

Consider the Clark equation, the case $\alpha=1$ of the delay difference equation … where $k$ is a fixed integer delay and $f:\mathbb R_+\to\mathbb R_+$ is smooth, decreasing, and…

Assume that $a\geq 0$ and that $f$ is an $S$-map. Let $K$ be the unique fixed point of $f$. Equation (1) has an equilibrium at $K$; a global attractor attracts the phase space, and…

Let $f$ be an $S$-map, let $K$ be the equilibrium of Equation (1), and let $\tau$ be its delay parameter. The equilibrium is locally asymptotically stable for sufficiently small…