Application of generalised Riccati equations to analysis of asymptotic forms of solutions of perturbed half-linear ordinary differential equations (Q2113765)

Summary: Asymptotic forms of solutions of half-linear ordinary differential equation \(\left(\left|u^\prime\right|^{\alpha - 1} u^\prime\right)^\prime = \alpha \left(1 + b \left(t\right)\right) \left|u\right|^{\alpha - 1} u\) 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.