Hilbert空间中的二阶微分方程问题  

Second-order Differential Equations in Hilbert Space

作　　者：马红铝[1] 薛星美[1] 

机构地区：[1]东南大学应用数学系,江苏南京210096

出　　处：《应用泛函分析学报》2004年第2期170-181,共12页Acta Analysis Functionalis Applicata

摘　　要：　运用多值分析、单调算子理论和Schauder不动点定理讨论了一类具有多点边值条件的二阶微分包含问题.作为一个预备性的结果,给出了一类二阶发展方程的解的存在唯一性和对初值的连续依赖性.最后,给出了以上结论在最优化和偏微分方程方面的两个应用.We consider a nonlinear second-order differential inclusion with a convex-valued term and nonlinear multivalued boundary conditions. Using the Schauder fixed-point theorem and techniques from multivalued analysis and from monotone operators theories, we prove the existence of a solution. As a preliminary step, we established the existence, uniqueness and continuous dependence upon data of solutions to a second-order evolution equation. Examples of problems for optimization and PDE are also discussed.

关 键 词：HILBERT空间 二阶微分方程 算子 极大单调 紧集 等度连续 多值分析 SCHAUDER不动点定理 

分 类 号：O175.15[理学—数学]