一类隐预解动力系统问题

A Class of Generalized Set-Valued Quasi-variational Inclusions and Implicit Resolvent Dynamical Systems

本文引入了H ilbert空间中一类广义集值变分包含问题,利用这类广义集值拟变分包含问题与预解方程及不动点问题间的等价性,建立了与这类广义集值拟变分包含问题有关的隐预解动力系统,给出了H ilbert空间中这类广义集值拟变分包含隐预解动力系统的解的存在性和收敛性定理,并指出了这类隐预解动力系统的解的轨道整体、指数地收敛于H ilbert空间中广义集值拟变分包含问题的唯一解.这些结果改进、推广和统一了文[1-8]的相应结果.

In this paper, by using the equivalence between a class of generalizied set-valued quasi-variational inclusions problem and implicit resolvent equations, fixed point problems, a class of implicit resolvent dynamical systems associated with quasi-variational inclusions in Hilbert spaces is suggested, and the trajectory of the solutions of the implicit dynamical system converges globally exponentially to the unicue solution of this setvalued quasi-variational indusion is also given. The results extend, improve and unify the corresponding results of [1-8].