Uniqueness and stability of slowly oscillating periodic solutions of delay equations with bounded nonlinearity (Q1181794)

The author studies the slowly oscillating periodic solutions of the following delay equation with small parameter: (1) \(-\varepsilon x'(t)=\sigma x(t)-f(x(t-1))\), where \(\varepsilon>0\), \(\sigma\geq 0\) are parameters. Under certain hypotheses on \(\varepsilon,\sigma\) and \(f\) the equation (1) has exactly one slowly oscillating periodic solution which is linearly stable.