Hilbert空间中的二阶微分方程问题

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．

Second-order Differential Equations in Hilbert Space

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.