Nonpivot and Implicit Projected Dynamical Systems on Hilbert Spaces

This paper presents a generalization of the concept and uses of projected dynamical systems to the case of nonpivot Hilbert spaces. These are Hilbert spaces in which the topological dual space is not identified with the base space. The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.

Some solvability theorems for nonlinear equations with applications to projected dynamical systems

We present in this paper some solvability results with applications to the study of existence of periodic orbits for projected dynamical systems. .