  In this paper, we study a class of singular double phase problems defined on
Minkowski spaces in terms of Finsler manifolds and with right-hand sides that
allow a certain type of critical growth for such problems. Under very general
assumptions and based on variational tools we prove the existence of at least
one nontrivial weak solution for such a problem. This is the first work dealing
with a Finsler double phase operator even in the nonsingular case.
