2017
Том 69
№ 9

All Issues

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

Sugie J., Yamaoka N.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 12, pp 1935-1949.

Citation Example: Sugie J., Yamaoka N. Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations // Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1704–1714.

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