[1]王卫勤.渐近正线性Duffing方程的非平凡解[J].南京师范大学学报(自然科学版),2012,35(02):29-31.
 Wang Weiqin.Nontrivial Solutions for Asymptotically Positive Linear Duffing Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(02):29-31.
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渐近正线性Duffing方程的非平凡解()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第35卷
期数:
2012年02期
页码:
29-31
栏目:
数学
出版日期:
2012-06-20

文章信息/Info

Title:
Nontrivial Solutions for Asymptotically Positive Linear Duffing Equations
作者:
王卫勤12
( 1. 泰州师范高等专科学校数理信息学院,江苏泰州225300) ( 2. 南京师范大学数学科学学院,江苏南京210046)
Author(s):
Wang Weiqin12
1.Dept of Math,Taizhou Teachers College,Taizhou,225300,China
关键词:
渐近正线性Duffing 方程非平凡解的存在性正线性Duffing 方程的分类理论Fuˇck 谱同伦连续方法
Keywords:
asymptotically positive linear Duffing equationsexistence of nontrivial solutionsclassification theory of positively linear Duffing equationsFuˇck spectrumhomotopy continutation method
分类号:
O175
摘要:
主要研究渐近正线性Duffing方程x″+f(t,x)=0,x(0)cosα-x’(0)sinα=0,x(1)cosβ-x’(1)sinβ=0非平凡解的存在性.首先介绍了满足Sturm-Liouville边值条件正齐次Duffing方程x″+q+(t)x+-q-(t)x-=0,x(0)cosα-p(0)x’(0)sinα=0,x(1)cosβ-p(1)x’(1)sinβ=0的分类理论,在此基础上讨论了渐近正线性Duffing方程非平凡解的存在性.在讨论时主要运用了相应的正齐次方程的分类理论及其相关的拓扑度方面的结果.
Abstract:
In this paper we mainly study the nontrivial solutions for asymptotically positive linear Duffing equations: x″ + f( t,x) = 0, x( 0) cosα - x’( 0) sinα = 0, x( 1) cosβ - x’( 1) sinβ = 0. We first introduce the classification theory of homogenous Sturm - Liouville boundary value problem for positively linear Duffing equations: ( p( t) x’( t) ) ’ + q + ( t) x + - q - ( t) x - = 0, x( 0) cosα - p( 0) x’( 0) sinα = 0, x( 1) cosβ - p( 1) x’( 1) sinβ = 0 and then investigate the existence of nontrivial solutions of asymptotically positive linear Duffing equations. The main methods in the discussion are the classification theory of linear homogenous equations and some results of the Leray- Schauder degree.

参考文献/References:

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[9] 王卫勤. 渐近正线性Duffing 的非平凡解[D]. 南京: 南京师范大学数学科学学院, 2008.
[10] Mawhin J. Topological degree methods in nonlinear boundary value problems[C]/ / CBMS Regional Conference Series in Mathematics,No. 40. Providence: Amer Math Soc, 1979.

备注/Memo

备注/Memo:
基金项目: 泰州师范高等专科学校校级青年专项重点课题( 2010-BSL-05) .
通讯联系人: 王卫勤,硕士,讲师,研究方向: 微分方程、几何等. E-mail: jswwqin@163. com
更新日期/Last Update: 2013-03-11