A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The works well in non-relativistic case, i.e., Laplacian operator. Here, we study how can be applied to Dirac operators. While this has successfully been done already one space dimension, and more generally codimension-1 boundaries, situati...

This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order ordinary differential equations and two-point, periodic boundary conditions. The methods involve novel differential inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution. AMS 2000 Classification: 34B15

In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas involve differential inequalities and Schaefer's fixed-point theorem.

We study the existence of solutions for a class of fractional differential inclusions with anti-periodic boundary conditions. The main result of the paper is based on Bohnenblust-Karlins fixed point theorem. Some applications of the main result are also discussed.