-properness and fixed point theorems for dissipative type maps.
In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].
In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.
We give an example of uniformly rotund in every direction space for which the minimal displacement characteristic is maximal.
In the paper a new proof of Lemma 11 in the above-mentioned paper is given. Its original proof was based on Theorem 3 which has been shown to be incorrect.