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Asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Sokea Luey, Hiroyuki Usami (2021)

Archivum Mathematicum

Asymptotic forms of solutions of half-linear ordinary differential equation ( | u ' | α - 1 u ' ) ' = α ( 1 + b ( t ) ) | u | α - 1 u are investigated under a smallness condition and some signum conditions on b ( t ) . When α = 1 , our results reduce to well-known ones for linear ordinary differential equations.

Asymptotic properties of one differential equation with unbounded delay

Zdeněk Svoboda (2012)

Mathematica Bohemica

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.

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