  The paper concerns the existence of normalized solutions to a large class of
quasilinear problems, including the well-known Born-Infeld operator. In the
mass subcritical cases, we study a global minimization problem and obtain a
ground state solution for a $(2,q)$-type operator which implies the existence
of solutions to the Born-Infeld problem. We also deal with the mass critical
and mass supercritical cases for quasilinear problems involving the
$(2,q)$-type operator.
