Normalized solutions for INLS equation with critical Hardy-Sobolev type nonlinearities

We are interested in finding prescribed L²-norm solutions to inhomogeneous nonlinear Schr\"odinger (INLS) equations. For N 3 we treat the equation with combined Hardy-Sobolev power-type nonlinearities - u+ u=|x|^-b|u|^q-2u+|x|^-d|u|^2^*₃-2u \;\;in\;\; RN, \, N 3 where, >0, 0<b, d<2, 2+ (4-2b) /N<q<2+ (4-2b) / (N-2) and 2^*₃= 2 (N-d) / (N-2) is the Hardy-Sobolev critical exponent, while for N=2 we investigate the equation with critical exponential growth equation aligned \;in\;\; R² aligned equation where the nonlinearity f (s) behaves like (s²) as s. We extend the existence results due to Alves-Ji-Miyagaki (Calc. Var. 61, 2022) from b =d= 0 to the case 0 < b, d < 2.