PROPERTY （X^＋） FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS OF GENERALIZED EULER TYPE

In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub（sup...

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Bibliographic Details
Published in:数学物理学报：B辑英文版 2013 (5), p.1398-1406
Main Author: Asadollah A GHAJANI Vahid ROOMI
Format: Article
Language:English
Subjects:
二阶非线性微分方程
充分条件
平面系统
广义非线性
振荡理论
物业
线性假设
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Summary:In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub（super） linearity are assumed. W＇e present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property （X^＋）, which is very important for the existence of periodic solutions and oscillation theory.
ISSN:0252-9602
1572-9087