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We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that any sweeping processes with almost periodic monotone right-hand-sides admits a globally exponentially stable almost periodic solution. And then we describe the extent to which such a globally stable solution persists under non-monotone perturbations. [ABSTRACT FROM AUTHOR]

[Display omitted] • A high-performance amorphous FeOOH-based anode is developed for Li-ion batteries. • One-step atmospheric plasma-assisted synthesis of FeOOH composite with graphite. • A capacity of ∼ 750 mAh g−1 is sustained after 500 cycles at 0.3 A g−1. • A capacity of ∼ 550 mAh g−1 is sustained after 2000 cycles at 1.2 A g−1. Iron oxide derivatives are promising materials for large-scale use as anode materials, owing to their natural abundance, inexpensiveness, and high theoretical capacity. Here, we synthesized amorphous urchin-like FeOOH nanoparticles and their graphite composite (FeOOH/Gr) in a one-step atmospheric plasma-assisted procedure and employed it in anode materials for Li-ion batteries. The obtained FeOOH nanoparticles are up to 300 nm in diameter with a needle thickness of about (3–10) nm, while FeOOH/Gr composite consists of graphite sheets covered with FeOOH needles. The FeOOH and FeOOH/Gr materials show excellent electrochemical performance as anode materials, with 633 mAh g−1 and 740 mAh g−1 at 0.3 A g−1 after 500 cycles, 353 mAh g−1 and 542 mAh g−1 at 1.2 A g−1 after 2000 cycles, respectively. By analyzing the state of the material at various stages of their life, we identify electrochemical milling as the performance-boosting process responsible for the 277% specific capacity increase during charge-discharge cycling after 50 cycles. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we provide a new result of the existence of equilibria for set-valued maps on bounded closed subsets of Hilbert spaces. We do not impose either convexity or compactness assumptions on but we assume that has epi-Lipschitz sections, i.e. its intersection with suitable finite dimensional spaces is locally the epigraph of Lipschitz functions. In finite dimensional spaces, the famous Brouwer theorem asserts the existence of a fixed point for a continuous function from a compact convex set to itself. Our result could be viewed as a kind of generalization of this classical result in the context of Hilbert spaces and when the function (or the set-valued map) does not necessarily map into itself ( is not invariant under the map). Our approach is based firstly on degree theory for compact and for condensing set-valued maps and secondly on flows generated by trajectories of differential inclusions. [Copyright &y& Elsevier]

We consider a system of two semilinear parabolic inclusions depending on a small parameter ϵ>0 which is present both in front of the derivative in one of the two inclusions and in the nonlinear terms to model high-frequency inputs.The aim is to provide conditions in order to guarantee, for ϵ>0 sufficiently small, the existence of periodic solutions and in order to study their behaviour as ϵ tends to zero. Our assumptions permit the definition of upper semicontinuous, convex valued, compact vector operators whose fixed points represent the sought-after periodic solutions. The existence of fixed points is shown by using topological degree theory arguments. [Copyright &y& Elsevier]