Differential equations on closed subsets of a probabilistic normed space

This paper is concerned with the problem of existence of solutions to the initial value problemu′(t) = A(t,u(t)), u(a) = z in a probabilistic normed space, whereA : [a, b) × D → E is continuous,D is a closed subset of a probabilistic normed spaceE, andz ? D. With a dissipative type condition onA, we estabilish sufficient conditions for this initial value problem to have a solution.