Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations - Sugie, J.; Yamaoka, N. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
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 $x eq 0$, but we do not necessarily require that $g (x)$ be monotone increasing. The obtained results are best possible in a certain sense. To establish our results, we use Sturm’s comparison theorem for linear Euler differential equations and phase plane analysis for a nonlinear system of Liénard type.