确定性与随机哈密顿方程边值问题中的特征值问题(英文)

Problem of Eigenvalues of Deterministic and Stochastic Hamiltonian Systems withBoundary Conditions

讨论给定边值条件下的确定性与随机哈密顿方程中的特征值问题．在一个适当的 Ｈｉｌｂｅｒｔ 空间里引入了一个新的单调算子．并且证明了这种特征值问题可以当作这个算子的谱问题来处理．这种处理方式可以利用泛函分析中的特征值理论的丰富结果来讨论随机微分方程边值问题的多解情况．并可用于处理随机优化问题．

The problem of spectrum and eigenvalues of deterministic and stochastic Hamiltonian systems, with two point boundary values conditions is discussed.A new monotone operator A in a suitable Hilbert space is introduced and shows that both problems can be treated as the problem of spectrum and eigenvalues of this A . This new observation permits us to profit very rich results in the theory of spectrum analysis to study the problem of multi solutions. The above mentioned equations contain two important systems as special cases:deterministic and stochastic Hamiltonian systems in mechanics and optimal control.