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

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.