Title: Application of generalised Riccati equations to analysis of asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Authors: Sokea Luey; Hiroyuki Usami

Addresses: Graduate School of Engineering, Gifu University, Gifu, 501-1193, Japan ' Faculty of Engineering, Gifu University, Gifu, 501-1193, Japan

Abstract: Asymptotic forms of solutions of half-linear ordinary differential equation (|u′|^α-1u′)′ = α(1 + b(t))|u|^α-1 u are investigated under smallness conditions on b(t). The proof of the main result is based on analysis of solutions of generalised Riccati equations related to this half-linear equation.

Keywords: half-linear ordinary differential equation; asymptotic form; Riccati equation; positive solution; perturbation theory; asymptotic behaviour.

DOI: 10.1504/IJDSDE.2021.117360

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.378 - 390

Received: 18 Jun 2020
Accepted: 02 Oct 2020
Published online: 01 Sep 2021 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article