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一类二阶渐近周期微分方程的正同宿轨道
引用本文:王为民,吴绍平.一类二阶渐近周期微分方程的正同宿轨道[J].高校应用数学学报(英文版),2002,17(1):7-12.
作者姓名:王为民  吴绍平
作者单位:Wang Weimin 1,2 Wu Shaoping 11 Dept.of Math.,Zhejiang Univ.,Hangzhou 310027. 2 Dept. of Appl. Math.,Zhejiang Univ. of Technology,Hangzhou 310034.
基金项目:ZJNSF(1 0 0 0 0 5 )
摘    要:§ 1 IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up,  x∈ R,( 1 )where1
关 键 词:系数泛函  变化性  渐近可展函数  微分方程

Positive homoclinic orbits for a class of asymptotically periodic second order differential equations
Wang?Weimin,Wu?Shaoping.Positive homoclinic orbits for a class of asymptotically periodic second order differential equations[J].Applied Mathematics A Journal of Chinese Universities,2002,17(1):7-12.
Authors:Wang Weimin  Wu Shaoping
Institution:(1) Dept. of Math., Zhejiang Univ., 310027 Hangzhou;(2) Dept. of Appl. Math., Zhejiang Univ. of Technology, 310034 Hangzhou
Abstract:This note studies the existence of positive homoclinic orbits of the second order equation

$$ - u' + \alpha (x)u = \beta (x)u^q  + \gamma (x)u^p ,x \in R,$$
(1)
where 1<q<p. Assume that the coefficient functions a(x), β(x) and γ(x) are asymptotically periodic and satisfy

$$0 < a \leqslant \alpha (x),   0 < \gamma (x) \leqslant B,    - M \leqslant \beta (x) \leqslant M.$$
(1)
A positive homoclinic orbit of the equation is obtained by means of variational methods. This research is supported by ZJNSF (100005).
Keywords:asymptotical period  differential equation  homoclinic orbit  
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