Exponential solutions of equation \(\dot y(t)=\beta(t)[y(t-\delta)-y(t-\tau)]\)
The authors study the asymptotic behaviour as \(t\to\infty\) of the first-order differential equation with two deviating arguments \[ \dot y= \beta(t)[y(t -\delta)- y(t- \tau)].\tag{\(*\)} \] The relation between solutions of \((*)\) and of the inequality \[ \dot y\leq\beta(t)[y(t- \delta)- y(t- \tau)]\tag{\(**\)} \] plays a basic role. A criterion for representing solutions of \((*)\) in exponential form is obtained. A sufficient condition for the existence of unbounded solutions is derived, and an illustrative example is given.
scientific article; zbMATH DE number 2085927