Convergence of the solutions of the equation y˙(t)=β(t)[y(<

Abstract

Convergence of the solutions of the equatioṅWe study the asymptotic behavior of the solutions of the first order differential equation containing two delaysẏThe convergence of all solutions is characterized by the existence of a strictly increasing bounded solution. A critical case is found for the coefficient function β. For coefficients below the critical function a strictly increasing and bounded solution is constructed, and thus the convergence of all solutions is shown. Relations with known results are discussed, too.