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OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING
作者姓名:罗辉  庄容坤  郭兴明
作者单位:Department of Mathematics,Huizhou College,Huizhou 516015,Guangdong Province,P.R.China,Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,P.R.China,Department of Mathematics,Huizhou College,Huizhou 516015,Guangdong Province,P.R.China
基金项目:ProjectsupportedbytheNaturalScienceFoundationofGuangdongProvinceofChina
摘    要:1IntroductionandProblem Thefollowingisthesecondordernonlineardifferentialequationwithdamping: p(t)ψ(y)u(y′)]′ r(t)y′(t) q(t)f(y)g(y′)=0(t≥t0),(1) inwhich,p(t)∈C′(t0,∞),(0,∞)),r(t)∈C(t0,∞),(-∞,∞)),q(t)∈C(t0, ∞),0,∞))withtheexistenceofT≥t0,q(t)≠0,t∈T,∞),f(y),g(y),ψ(y),u(y) ∈C((-∞,∞),(-∞,∞)),andyf(y)>0,yu(y)>0,y≠0. Thesolutiony(t)ofEq.(1)iscallednormalsolutionify(t)isthenon_constantsolutionof Eq.(1)andsupt≥t0|y(t)|>0(refertoRef.1]).Anormalsolutionisoscill…

关 键 词:二阶非线性微分方程  阻尼振动  里卡提变换  积分平均化
收稿时间:25 October 2003

Oscillation criteria for second order nonlinear differential equation with damping
Luo Hui,Zhuang Rong-kun,Guo Xing-ming.OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING[J].Applied Mathematics and Mechanics(English Edition),2005,26(4):441-448.
Authors:Luo Hui  Zhuang Rong-kun  Guo Xing-ming
Institution:1. Department of Mathematics, Huizhou College, Huizhou 516015, Guangdong Province, P.R. China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China
2. Department of Mathematics, Huizhou College, Huizhou 516015, Guangdong Province, P.R. China
3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China
Abstract:By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
Keywords:second order nonlinear differential equation with damping  oscillation  Riccati transformation  integral averaging technique
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