On solutions of \(x''=-e^{\alpha \lambda t}x^{1+\alpha}\)
type: Item
instance of: scholarly article
title: On solutions of \(x''=-e^{\alpha \lambda t}x^{1+\alpha}\)
zbMATH Open document ID: 0693.34066
author: Ichiro Tsukamoto
published in: Tokyo Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The nonlinear differential equations \[ \frac{d}{dt}(t^ p\frac{du}{dt})+t^ su^ n=0\quad and\quad \frac{d}{dt}(t^ p\frac{du}{dt})-t^ su^ n=0 \] are the starting point. These equations can be transformed into four differential equations. The author considers one - that means the last - case of the for cases. By the transformation \(y=-\lambda^{-2}e^{\alpha \lambda t}\phi^{\alpha},\) \(z=y'\) and \(\phi\) is an arbitrary solution of the given equation you get a first order algebraic differential equation and you can start to discuss the asymptotic behavior of solutions.
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 4134512
zbMATH Keywords: first order algebraic differential equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133557
OpenAlex ID: W2035625820
DOI: 10.3836/TJM/1270133557
description: scientific article; zbMATH DE number 4134512