Geodesic
Asymptotic properties of one differential equation with unbounded delay
Mathematica Bohemica, Tome 137 (2012) no. 2, pp. 239-248

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MR Zbl
We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.
We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.
DOI : 10.21136/MB.2012.142869
Classification : 34A25, 34E05, 34K25, 47N20
Keywords: asymptotic expansion; retract method 
Svoboda, Zdeněk. Asymptotic properties of one differential equation with unbounded delay. Mathematica Bohemica, Tome 137 (2012) no. 2, pp. 239-248. doi: 10.21136/MB.2012.142869
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