  In this paper, we study the existence and multiplicity problems for
orthogonal Finsler geodesic chords in a manifold with boundary which is
homeomorphic to a N-dimensional disk. Under a suitable assumption, which is
weaker than convexity, we prove that, if the Finsler metric is reversible, then
there are at least N orthogonal Finsler geodesic chords that are geometrically
distinct. If the reversibility assumption does not hold, then there are at
least two orthogonal Finsler geodesic chords with different values of the
energy functional.
