Further results on the existence of periodic solutions to DDES with multiple lags (Q1806069)

The paper deals with periodic solutions to \[ x'(t)= \sum^n_{i=1} \delta_i f(x(t- s_i)),\quad t\in\mathbb{R},\quad x\in\mathbb{R},\tag{\(*\)} \] with \(\delta_i= 1\) or \(-1\), \(0<s_i\) are constants, \(f\in C^0(\mathbb{R},\mathbb{R})\), \(f\) odd, \(xf(x)> 0\) for \(x\neq 0\), \(\lim_{x\to 0}f(x)/x= \alpha\), \(\lim_{x\to\infty} f(x)/x= \beta\). The delays in \((*)\) and properties of \(f\) enable to find periodic solutions to \((*)\) with periods connected with \(s_i\), \(n\) and \(m_i\in \mathbb{N}\). Five criteria for the existence of periodic solutions are given.