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# Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$Originální název Unbounded solutions of the equation$\dot y(t)=\sum_{i=1}^{n}\beta_{i}$(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$

Anglický název

Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$Jazyk en Originální abstrakt Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the form$\dot y(t)=\sum_{i=1}^{n}\beta_{i}(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$is discussed for$t\to\infty$. A criterion for representing solutions in exponential form is proved. Inequalities for solution estimation are given. Sufficient conditions for the existence of unbounded solutions are derived. A relevant illustrative example is given as well. Known results are discussed and compared. Anglický abstrakt Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the form$\dot y(t)=\sum_{i=1}^{n}\beta_{i}(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$is discussed for$t\to\infty$. A criterion for representing solutions in exponential form is proved. Inequalities for solution estimation are given. Sufficient conditions for the existence of unbounded solutions are derived. A relevant illustrative example is given as well. Known results are discussed and compared. BibTex  @article{BUT103938, author="Josef {Diblík} and Miroslava {Růžičková} and Radoslav {Chupáč}", title="Unbounded solutions of the equation$\dot y(t)=\sum_{i=1}^{n}\beta_{i}$(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$",
annote="Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the form $\dot y(t)=\sum_{i=1}^{n}\beta_{i}(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$ is discussed for  $t\to\infty$. 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.",
}