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

摘要: 本文研究弹性染方程边值共振问题-d⁴u/dx⁴+π⁴u+g(x,u)=e(x)(0R→R满足Carathéodory条件,e∈L²[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.
- 多解结果 /
- 弹性梁方程 /
- 共振 /
- 集连通技巧
Abstract: This paper deals with multiplicity results for nonlinear elastic equations of the type -d⁴u/dx⁴+π⁴u+g(x,u)=e(x)(0R→R satisfies Carathéodory condition 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 procedure with the technique of connected set,we establish several multiplicity results under suitable condition.
- multiplicity results /
- elastic beam equations /
- resonance /
- technique of connected set

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