Unbounded solutions of the equation ẏ(t)=∑i=1nβi(t)y(t-δi)-y(t-τi)

Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the formẏ(t)=∑i=1nβi(t)y(t-δi)-y(t-τi)is discussed for t→∞. A criterion for representing solutions in exponential form is proved. Inequalities for solution estimation are given. Sufficient conditions for the existence of unbounded solutions are derived. A relevant illustrative example is given as well. Known results are discussed and compared.