An affine Birkhoff–Kellogg-type result in cones with applications to functional differential equations

In this short note, we prove, by means of classical fixed point index, an affine version of a Birkhoff–Kellogg-type theorem in cones. We apply our result to discuss the solvability of a class of boundary value problems for functional differential equations subject to functional boundary conditions. We illustrate our theoretical results in an example