Battery Energy Storage System (BESS) is one of the potential solutions to increase energy system flexibility, as BESS well suited solve many challenges in transmission and distribution networks. Examples network’s challenges, which affect network performance, are: (i) Load disconnection or technical constraints violation, may happen during reconfiguration after fault, (ii) Unpredictable power g...

We consider whether the “inequality-splitting” property established in the Brøndsted– Rockafellar theorem for the subdifferential of a proper convex lower semicontinuous function on a Banach space has an analog for arbitrary maximal monotone multifunctions. We introduce the maximal monotone multifunctions of type (ED), for which an “inequality-splitting” property does hold. These multifunctions...

Solutions of the Hamilton-Jacobi equation H(x,−Du(x)) = 1, with H(·, p) Hölder continuous and H(x, ·) convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the C-regularity of the extremal trajectories associated with the multifunction generated by DpH .

The objective of this paper is to obtain the properties of αψcompact spaces by using nets, filterbase, αψ-complete accumulation points and so on. We also investigate some properties of αψ-continuous multifunctions and αψ-compact spaces in the context of multifunction.

Let F be a multifunction from a metric space X into L, and B a subset of X . We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F (x) for x ∈ B.