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.