In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire’s category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch. 1991 Mathematics Subject Classification: Primary 49J52.

Traveling wave solutions of reaction-diffusion equations are well studied for Lipschitz continuous monostable and bistable reaction functions. These special play a key role in mathematical biology particular the study ecological invasions. However, if there more than two stable steady states, invasion phenomenon may become intricate involve intermediate steps, which leads one to consider not si...

In this paper we look at the properties of limits of a sequence of real valued inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However, we show that as long as the drift terms satisfy a Lipschitz condition and the limit is continuous in probability, then it will lie in a class of processes that w...