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

We are interested in finding prescribed L²-norm solutions to inhomogeneous nonlinear Schr\"{o}dinger (INLS) equations. For N≥ 3 we treat the equation with combined Hardy-Sobolev power-type nonlinearities -Δ u+λ u=μ|x|⁻ᵇ|u|q-2u+|x|⁻ᵈ|u|^2^*d-2u \;\;in\;\; RN,\, N≥ 3 where λ, μ>0, $0<b,d<2$, $2+(4-2b)/N<q<2+(4-2b)/(N-2)$ and 2^*d= 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} &-Δ u+λ u=|x|⁻ᵇf(u) \;\;in\;\; R^2 {aligned} {equation} where the nonlinearity $f(s)$ behaves like exp(s²) as s→∞. We extend the existence results due to Alves-Ji-Miyagaki (Calc. Var. 61, 2022) from $b =d= 0$ to the case $0 < b,d < 2$.