Title: Comparison results for first order linear operators with reflection and periodic boundary value conditions,
Abstract: This work is devoted to the study of the first order operator
$x'(t)+m\,x(-t)$ coupled with periodic boundary value conditions. We describe
the eigenvalues of the operator and obtain the expression of its related
Green's function in the non resonant case. We also obtain the range of the
values of the real parameter $m$ for which the integral kernel, which provides
the unique solution, has constant sign. In this way, we automatically establish
maximum and anti-maximum principles for the equation. Some applications to the
existence of nonlinear periodic boundary value problems are showed.