On a problem of I. Györi
The paper deals with the equation (1) \(x'(t)= -x(t-\tau(t))\), where \(\tau(t)\geq 0\) is a continuous function on \([t_ 0,\infty)\) and \(t_ 0\) is some constant. The author presents a necessary and sufficient condition for (1) to possess a positive solution corresponding to \(t_ 0\) and disproves I. Györi's conjecture that the condition \(\tau(t)\leq e^{-1}\) for \(t\geq t_ 0\) is necessary for existence of positive solutions of (1) corresponding to \(t_ 0\).
scientific article; zbMATH DE number 599922