Exponential solutions of equation

Abstract

Asymptotic behaviour of solutions of first-order differential equation with two deviating arguments of the form y ̇ (t)=β(t) y(t−δ)−y(t−τ) is discussed for t →∞. A criterion for representing solutions in exponential form is proved. As consequences, inequalities for such solutions are given. Connections with known results are discussed and a sufficient condition for existence of unbounded solutions, generalizing previous ones, is derived. An illustrative example is considered, too.