  The n-dimensional extension of the one dimensional Position-dependent mass
(PDM) Lagrangians under the nonlocal point transformations by Mustafa
<cite>38</cite> is introduced. The invariance of the n-dimensional PDM
Euler-Lagrange equations is examined using two possible/different PDM
Lagrangian settings. Under the nonlocal point transformation of Mustafa
<cite>38</cite>, we have shown that the PDM Euler-Lagrange invariance is only
feasible for one particular PDM-Lagrangians settings. Namely, when each
velocity component is deformed by some dimensionless scalar multiplier that
renders the mass position-dependent. Two illustrative examples are used as
reference Lagrangians for different PDM settings, the nonlinear n-dimensional
PDM-oscillators and the nonlinear isotonic n-dimensional PDM-oscillators. Exact
solvability is also indulged in the process.
