*Correspondence: [email protected] 2Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract We will present an up-to-date review on anti-periodic boundary value problems of fraction...

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic pl...

A model of flow passing through the glottis is presented by employing the boundary-layer assumption. A thin boundary layer near the glottal wall influences the flow behavior in terms of the flow separation, jet formation, and pressure distribution along the channel. The integral momentum relation has been developed to analyze the boundary layer accurately, and it can be solved numerically for t...

Equilibration times for nuclear matter configurations – modelling intermediate and high energy nucleus-nucleus collisions – are evaluated within the semiclassical off-shell transport approach developed recently. The transport equations are solved for a finite box in coordinate space employing periodic boundary conditions. The off-shell transport model is shown to give proper off-shell equilibri...

We derive Bogomolny-type equations for the Abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in noncommutative space and discussed how vortex solutions are constructed. We also consider the extension to an U(2)×U(1) model, a simplified prototype of the noncommutativ...

Let IR 2 be a bounded domain that is smooth except for a nite number of corners. The aim of this paper is to obtain conditions such that the solution of the Poisson problem ?u = f 0 in (f 6 = 0), with zero Dirichlet boundary condition, behaves similarly at the boundary as does the rst eigenfunction 1. That is: there exist c 1 ; c 2 > 0 such that c 1 1 (x) u (x) c 2 1 (x) : As a consequence we c...

We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency pr...

A new theorem is applied to the Kuramoto-Sivashinsky equation with L-periodic boundary conditions, proving the existence of an asymptotically complete inertial manifold attracting all initial data. Combining this result with a new estimate of the size of the globally absorbing set yields an improved estimate of the dimension, N ∼ L.

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

We study a linear fractional differential equation with a periodic boundary condition and give the explicit form of the solution and the corresponding Green’s function. Using some properties of the Green’s function we present some new comparison results.