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Exponential solutions of equation $\dot y(t)=\beta(t)[y(t-\delta)-y(t-\tau)]$. (English) Zbl 1058.34099
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 $$\dot y\le\beta(t)[y(t- \delta)- y(t- \tau)]\tag{$**$}$$ 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.

34K25Asymptotic theory of functional-differential equations
Full Text: DOI
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