一维非线性梁振动方程周期解的存在性  

Existence of Periodic Solutions to 1D Nonlinear Beam Equations

作　　者：唐秋林[1] 耿建生[2] 吴美云[1] 

机构地区：[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,山东滨州256604

出　　处：《南通工学院学报》2001年第3期51-53,共3页Journal of Nantong Institute of Technology

摘　　要：对一维非线性梁振动方程上满足铰链边界条件，其中为解析的奇函数，文章证明了对于大多数的ｍ２，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．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.

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 

分 类 号：O175.29[理学—数学] O326[理学—基础数学]