Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations

• Date: 2006
• Main Authors: Sugie, J., Yamaoka, N., Суґіе, Й., Ямаока, Н.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3566
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The purpose of this paper is to present new oscillation theorems and nonoscillation theorems for the nonlinear Euler differential equation $t^2 x″' + g (x) = 0$. Here we assume that $x g(x) > 0$ if $x \neq 0$, but we do not necessarily require that $g (x)$ be monotone increasing. Th...