弹性梁方程共振问题的几个多解存在定理  

Some Multiplicity Results for an Elastic Beam Equation at Resonance

作　　者：马如云[1] 

机构地区：[1]西北师范大学

出　　处：《应用数学和力学》1993年第2期180-188,共9页Applied Mathematics and Mechanics

摘　　要：本文研究弹性染方程边值共振问题-d^4u/dx^4+π~4u+g(x,u)=e(x) (0<x<1)u(0)=u(1)=u~＂(0)=u~＂(1)=0其中g:[0,1]×R→R满足Carath(?)odory条件,e∈L^2[0,1].虽然该问题解的存在性曾有人研究过,但多解的存在性尚未被研究.在适当的假设下,利用Lyapunov-Schmidt过程及集连通技巧,我们得到该问题的几个多解存在定理.This paper deals with multiplicity results for nonlinear elastic equation of the type -where g-[0, 1]XR-,R satisfies Carathfiodory conditions e(L2[0, 1], The solvability of this problem has been studied by several authors, but there isn't any multiplicity result until now to the author's knowledge. By combining the Lyapunov-Schmidt procudure with the technique of cornectcd sot, we establish several multiplicity results under suitable conditions.

关 键 词：弹性 梁 弯曲 常微分方程 边值问题 

分 类 号：TU323.3[建筑科学—结构工程]