| 一维非线性梁振动方程周期解的存在性 |
| |
| 引用本文： | 唐秋林 耿建生 等. 一维非线性梁振动方程周期解的存在性[J]. 南通工学院学报(社会科学版), 2001, 17(3): 51-53 |
| |
| 作者姓名： | 唐秋林 耿建生 等 |
| |
| 作者单位： | [1]南通师范学院数学系，江苏南通226007 [2]滨州师范专科学校数学系，山东滨洲256604 |
| |
| 摘 要： | 对一维非线性梁振动方程utt uxxxx m^2u u^3 f(u)=0,在[0,π]上满足铰链边界条件，其中f(u)=∑^∞m=5fmu^5为解析的奇函数，文章证明了对于大多数的m^2，上述方程存在小振幅周期解。这个证明利用了Lyapunov-Schmidt分解及隐函数定理。
|
| 关 键 词： | 非线性梁 振动方程 周期解 奇异点 铰链边界条件 Lygpunou－Schmidt分解 稳函数定理 |
| 文章编号： | 1008-2190(2001)03-0051-03 |
Existence of Periodic Solutions to 1D Nonlinear Beam Equations |
| |
| TANG Qiu-lin,GENG Jian-sheng,WU Mei-yun. Existence of Periodic Solutions to 1D Nonlinear Beam Equations[J]. Journal Of Nantong University(Education Sciences Edition), 2001, 17(3): 51-53 |
| |
| Authors: | TANG Qiu-lin GENG Jian-sheng WU Mei-yun |
| |
| Abstract: | We prove the existence to periodic solutions to lD nonlinear beam equation satisfies the hinged boundary conditions on the interval ,and f(u) is an analytic odd function . It is proved that for most m2, the above equation admits small-amplitude periodic solutions. The proof is based on Lyapunov-Schmidt decomposition and implicit theorems. |
| |
| Keywords: | nonlinear beam equation periodic solution singular point |
| 本文献已被 CNKI 维普 等数据库收录！ |
