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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 PDMEuler-Lagrange equations is examined using two possible/different PDMLagrangian settings. Under the nonlocal point transformation of Mustafa<cite>38</cite>, we have shown that the PDM Euler-Lagrange invariance is onlyfeasible for one particular PDM-Lagrangians settings. Namely, when eachvelocity component is deformed by some dimensionless scalar multiplier thatrenders the mass position-dependent. Two illustrative examples are used asreference Lagrangians for different PDM settings, the nonlinear n-dimensionalPDM-oscillators and the nonlinear isotonic n-dimensional PDM-oscillators. Exactsolvability is also indulged in the process.

On the n-dimensional extension of Position-dependent mass Lagrangians: nonlocal transformations, Euler--Lagrange invariance and exact solvability