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

  • J. Sugie
  • N. Yamaoka


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. 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.
How to Cite
Sugie, J., and N. Yamaoka. “Multilayer Structures of Second-Order Linear Differential Equations of Euler Type and Their Application to Nonlinear Oscillations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 12, Dec. 2006, pp. 1704–1714,
Research articles