Periodic solutions of dissipative functional differential equations
In this paper we consider \(T\)-periodic finite delay differential equations. We investigate dissipativeness for these equations, which is a weaker condition than uniform ultimate boundedness. The later condition is usually used together with uniform boundedness to prove the existence of a \(T\)-periodic solution. The first two theorems prove dissipativeness for these equations generalizing a result of Pliss. Hale and Lopes proved a result that implies that a dissipative \(T\)-periodic finite delay equation has a \(T\)-periodic solution. Since this result is not very well known, we restate it and prove it in a short, elementary way. We also present a theorem using Lyapunov functionals to show the dissipativeness of a finite delay differential equation. We also give an example, which is dissipative but not uniformly ultimately bounded.
periodic finite delay differential equations
scientific article; zbMATH DE number 697063