third-order delay differential equations
On the asymptotic behavior of some nonlinear delay differential systems
Here, the author first investigates the existence of solutions for delay differential equations. The approach used to prove existence results is relatively original. The idea is to consider the delay terms as forcing terms for an ordinary differential equation. The second part of the paper is concerned with the convergence of the solutions to zero (which is an equilibrium) for \(t\to\infty\). In this second part, the author does not apply the existence results obtained in the first part, some known results for the example under consideration are exploited. Then by using global stability results for nonautonomous perturbations of a linear scalar ordinary differential equation, and some estimations, the author proves the convergence of positive solutions to zero.
scientific article; zbMATH DE number 1672652