In this paper we deal with a first order evolution inclusion involving multivalued term generated by Clarke subdifferential of locally Lipschitz potential. For problem construct double step time-semidiscrete approximation, known as the Rothe scheme. We study sequence solutions semidiscrete approximate problems and provide its weak convergence to limit element that is solution original problem.

Many interesting real functions on Euclidean space are differentiable almost everywhere. All Lipschitz functions have this property, but so, for example, does the spectral abscissa of a matrix (a non-Lipschitz function). In practice, the gradient is often easy to compute. We investigate to what extent we can approximate the Clarke subdifferential of such a function at some point by calculating ...

In this study, the multivalued fixed point theorem, Clarke subdifferential properties, fractional calculus, and stochastic analysis are used to arrive at system’s mild solution (1). Furthermore, mean square moment for aforementioned system (1) confirms conditions trajectory (T-)controllability. The last part of paper uses two numerical applications explain novel theoretical results that were re...

The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hy...

Let C be a nonempty closed subset of the real normed linear space X. In this paper we determine the extent to which formulas for the Clarke subdifferential of the distance for C, de(x) := inf I/Y.rll, be< which are valid when C is convex, remain valid when C is not convex. The assumption of subdifferential regularity for d, plays an important role. When x 4 C, the most precise results also requ...

This manuscript explores a new class of non-autonomous second-order stochastic inclusions Clarke?s subdifferential form with non-instantaneous impulses (NIIs), unbounded delay, and the Rosenblatt process in Hilbert spaces. The existence solution is deduced by employing fixed point strategy for set-valued map together evolution operator analysis approach. An example analyzed theoretical developm...