The stationary SchrrdingerrPoisson system with a selffconsistent eeective KohnnSham potential is a system of PDEs for the electrostatic potential and the envelopes of wave functions deening the quantum mechanical carrier densities in a semiconductor nanostructure. We regard both Poisson's and Schrrdinger's equation with mixed boundary conditions and discontinu-ous coeecients. Without an exchang...

This note continues the study initiated in 2006 by P.L. Papini, R. R. Phelps and the author on some classical notions from finite-dimensional convex geometry in spaces of continuous functions. Let H be the family of all closed, convex and bounded subsets of a Banach space endowed with the Hausdorff metric. A completion of A ∈ H is a diametrically maximal set D ∈ H satisfying A ⊂ D and diamA = d...

A metric space X has Markov type 2, if for any reversible finite-state Markov chain {Zt} (with Z0 chosen according to the stationary distribution) and any map f from the state space to X, the distance Dt from f(Z0) to f(Zt) satisfies E(D t ) ≤ K tE(D 1) for some K = K(X) < ∞. This notion is due to K. Ball (1992), who showed its importance for the Lipschitz extension problem. However until now, ...

Let E be a closed set in R, and suppose that there is a k ≥ 1 such that every x, y ∈ E can be connected by a rectifiable path in E with length ≤ k |x−y|. This condition is satisfied by chord-arc curves, Lipschitz manifolds of any dimension, and fractals like Sierpinski gaskets and carpets. Note that length-minimizing paths in E are chord-arc curves with constant k. A basic feature of this condi...

Generalized processor sharing has been proposed as a policy for distributing processing in a fair manner between diierent data classes in high-speed networks. In this paper we show how recent results on the Skorokhod Problem can be used to construct and analyze the mapping that takes the input processes into the buuer content. More precisely, we show how to represent the map in terms of a Skoro...

We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone and k-Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative s...

We are interested in existence results for nonconvex functional differential inclusions. First, we prove an existence result, in separable Hilbert spaces, for first order nonconvex sweeping processes with perturbation and with delay. Then, by using this result and a fixed point theorem we prove an existence result for second order nonconvex sweeping processes with perturbation and with delay of...

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...