We consider first order periodic differential inclusions in R . The presence of a subdifferential term incorporates in our framework differential variational inequalities in R . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.

Abstract In this paper, Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions are studied. By using calculus, analysis, properties of nonsmooth sufficient for controllability the considered problem established. Finally, an example is given to illustrate obtained results.

We revisit some basic concepts and ideas of the classical differential calculus convex analysis extending them to a broader frame. reformulate generalize notion Gateaux differentiability propose new notions generalized derivative subdifferential in an arbitrary topological vector space. Meaningful examples preserving key properties original are provided.

A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the qualification conditions in the context of different problem formulations in this area. We show that not only the meanwhile classical generalized interiorit...

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated i...