Convergence of the solutions of the equation \(\dot y(t) = \beta(t)[y(t-\delta)-y(t-\tau)]\) in the critical case
This paper deals with the asymptotic behavior of a first order linear homogeneous differential equation with double delay of the form \[ y'(t)=\beta(t)[y(t-\delta)-y(t-\tau)], \] where \(\delta\) and \(\tau\) are positive with \(\tau>\delta\); \(\beta\in C([t_0-\tau,\infty),\mathbb R^+)\). The authors especially deal with the so called critical case with respect to the function \(\beta\) which separates the case when all solutions are convergent and the case when there exist divergent solutions. For coefficients below the critical function, a strictly increasing and bounded solution is constructed, which characterizes the asymptotic convergence of all solutions.
scientific article; zbMATH DE number 5146744