[1]王卫勤.渐近正线性Duffing方程的非平凡解[J].南京师大学报(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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《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]
- 卷:
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第35卷
- 期数:
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2012年02期
- 页码:
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29-31
- 栏目:
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数学
- 出版日期:
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2012-06-20
文章信息/Info
- Title:
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Nontrivial Solutions for Asymptotically Positive Linear Duffing Equations
- 作者:
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王卫勤1; 2
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( 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):
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Wang Weiqin1; 2
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1.Dept of Math,Taizhou Teachers College,Taizhou,225300,China
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- 关键词:
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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:
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asymptotically positive linear Duffing equations; existence of nontrivial solutions; classification theory of positively linear Duffing equations; Fuˇck spectrum; homotopy continutation method
- 分类号:
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O175
- 摘要:
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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:
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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:
[1] Dong Y. On the solvability of asymptotically positively homogeneous equations with Sturm-Liouville boundary conditions[J]. Nonlinear Analysis,2000( 42) : 1 351-1 363.
[2] Ekeland I. Convexity Methods in Hamiltonian Mechanics[M]. Berlin: Springer,1990.
[3] Long Y. Index Theory for Symplectic Paths With Applications[M]. Birkhauser: Basel,2002.
[4] Fuˇck S. Solvability of Nonlinear Equations and Boundary Value Problems[M]. Boston: D Reidel,1980.
[5] Lazer A C,Leach D E. On a nonlinear two point BVP[J]. J Math Anal Appl,1969, 26: 20-27.
[6] 张恭庆. 临界点理论及其应用[M]. 上海: 上海科学技术出版社, 1986.
[7] 郭大钧. 非线性泛函分析[M]. 济南: 山东科学技术出版社, 1985.
[8] Mawhin J,Willem M. Critical Point Theory and Hamiltonian Systems[M]. Berlin: Springer,1989.
[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:
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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