Approximation from the exterior of a multifunction and its applications in the “sweeping process”

AbstractWe approximate from the exterior an upper semicontinuous multifunction C(·) from a metric space into the closed convex subsets of a normed space by means of globally Lipschitzean multifunctions; in particular, when C(·) is continuous, this approximation allows us to reduce the problem of the existence of solutions of the associated evolution equation to the case in which C(·) is Lipschitzean

Viable solutions of differential inclusions with memory in Banach spaces

In this paper we study functional differential inclusions with memory and state constraints. We assume the state space to be a separable Banach space and prove existence results for an upper semicontinuous orientor field; we consider both the case of a globally measurable orientor field and the case of a Caratheodory one

Existence of periodic orbits for vector fields via Fuller index and the averaging method

We prove a generalization of a theorem proved by Seifert and Fuller concerning the existence of periodic orbits of vector fields via the averaging method. Also we show applications of these results to Kepler motion and to geodesic flows on spheres

Synergistic Effect of Sn and Fe in Fe-Nx Site Formation and Activity in Fe-N-C Catalyst for ORR

Iron-nitrogen-carbon (Fe-N-C) materials emerged as one of the best non-platinum group material (non-PGM) alternatives to Pt/C catalysts for the electrochemical reduction of O2 in fuel cells. Co-doping with a secondary metal center is a possible choice to further enhance the activity toward oxygen reduction reaction (ORR). Here, classical Fe-N-C materials were co-doped with Sn as a secondary metal center. Sn-N-C according to the literature shows excellent activity, in particular in the fuel cell setup; here, the same catalyst shows a non-negligible activity in 0.5 M H2SO4 electrolyte but not as high as expected, meaning the different and uncertain nature of active sites. On the other hand, in mixed Fe, Sn-N-C catalysts, the presence of Sn improves the catalytic activity that is linked to a higher Fe-N4 site density, whereas the possible synergistic interaction of Fe-N4 and Sn-Nx found no confirmation. The presence of Fe-N4 and Sn-Nx was thoroughly determined by extended X-ray absorption fine structure and NO stripping technique; furthermore, besides the typical voltammetric technique, the catalytic activity of Fe-N-C catalyst was determined and also compared with that of the gas diffusion electrode (GDE), which allows a fast and reliable screening for possible implementation in a full cell. This paper therefore explores the effect of Sn on the formation, activity, and selectivity of Fe-N-C catalysts in both acid and alkaline media by tuning the Sn/Fe ratio in the synthetic procedure, with the ratio 1/2 showing the best activity, even higher than that of the iron-only containing sample (jk = 2.11 vs 1.83 A g-1). Pt-free materials are also tested for ORR in GDE setup in both performance and durability tests

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions

On the Upper Semicontinuity of the Hamiltonian

We give upper semicontinuity results for Fenchel's conjugate (with respect to v) of a function L(u,v)

On the existence of heteroclinic trajectories for asymptotically autonomous equations

By means of a minimax argument, we prove the existence of at least one heteroclinic solution to a scalar equation of the kind x''=a(t)V'(x), where V is a double well potential, 0<l<=a(t)<=L, a(t) converges to l as |t| diverges and the ratio L/l is suitably bounded from above

An Approximation Result for Integrands of the Calculus of Variations

We approximate from below an integrand L(t,u,v) by means of functions which enjoy Lipschitz properties with respect to u and v. Convexity on v is preserved