Let a given set be endowed with a preference preordering, and consider the problem of finding a solution to the differential inclusion A(OeS(*(O) which remains in the given set and evolves monotonically with respect to the preordering. We give sufficient conditions for the existence of such a trajectory, couched in terms of a notion of tangency developed by Clarke. No smoothness or convexity is...

A multifunction φ : X ( Y is n-valued if φ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps φ : S ( S are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(φ) of an n-valued φ : S ( S of degree d equals |n − d| and φ is homotopic to an n-valued power map ...

Let F:X-*X be a multifunction on a partially ordered set (X, ¿). Suppose for each pair «iá*2 and for each yi<EF(xi) there is a yi&F{y¿) such that yièyiThen sufficient conditions are given such that multifunctions F satisfying the above condition will have a fixed point. These results generalize the Tarski Theorem on complete lattices, and they also generalize some results of S. Abian and A. B. ...