Jarosław Mederski

Ground states of a system of nonlinear Schrödinger equations with periodic potentials

ABSTRACT We are concerned with a system of coupled Schrödinger equations where F and Vi are periodic in x and 0∉σ(−Δ+Vi) for i = 1,2,…,K, where σ(−Δ+Vi) stands for the spectrum of the Schrödinger operator −Δ+Vi. We impose general assumptions on the nonlinearity F with the subcritical growth and we find a ground state solution being a minimizer of the energy functional associated with the system on a Nehari–Pankov manifold. Our approach is based on a new linking-type result involving the Nehari–Pankov manifold.

Fixed point index for Krasnosel'skii-type set-valued maps on complete ANRs

In the paper a fixed-point index for a class of the so-called Krasnoselski{\u\i}-type set-valued maps defined locally on arbitrary absolute neighbourhood retracts is presented. Various applications to the existence problems for constrained differential inclusions and equations are provided.

Asynchronous parallel molecular dynamics simulations

Dynamic development of parallel computers makes them standard tool for large simulations. The technology achievements are not followed by the progress in scalable code design. The molecular dynamics is a good example. In this paper we present novel approach to the molecular dynamics which is based on the new asynchronous parallel algorithm inspired by the novel computer architectures. We present also implementation of the algorithm written in Java. Presented code is object-oriented, multithread and distributed. The performance data is also available.

Vortex ground states for Klein-Gordon-Maxwell-Proca type systems

We look for three-dimensional vortex-solutions, which have finite energy and are stationary solutions, of Klein-Gordon-Maxwell-Proca type systems of equations. We prove the existence of three-dimensional cylindrically symmetric vortex-solutions having a least possible energy among all symmetric solutions. Moreover we show that, if the Proca mass disappears, then the solutions tend to a solution of the Klein-Gordon-Maxwell system.