Nonlinear oscillations of second order differential equations of Euler type期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Nonlinear oscillations of second order differential equations of Euler type

Authors:	Jitsuro Sugie Tadayuki Hara

Institution:	Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan ; Department of Mathematical Sciences, University of Osaka Prefecture, Sakai 593, Japan

Abstract:	We consider the nonlinear equation $t^{2}x' + g(x) = 0$ , where satisfies for $x \ne 0$ , but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case $\frac {g(x)}{x} \to \frac {1}{4} \text {as} \|x\| \to \infty$ , which is most difficult.

Keywords:	Oscillation nonlinear differential equations Li\'{e}nard system global phase portrait

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