Normalized solution for quasilinear Schrödinger operators with general potentials: the Lᵖ-supercritical case

We establish the existence of a normalized solution for the following quasilinear elliptic problem: $${aligned} \{ {array}{cc} -Δ _p u + V(x) |u|ᵖ⁻²u = λ |u|p - 2u + | u| q-2u\ in\ R^N,\\ ∫ R^N |u|^p dx = m^p,\ u ∈ W1, p(R^N),{array}. {aligned}$$ - Δ p u + V ( x ) | u | p - 2 u = λ | u | p - 2 u + u q - 2 u in R N , ∫ R N | u | p d x = m p , u ∈ W 1 , p ( R N ) , where $$N > p$$ N > p , $$1< p< p+ p^2/N< q < p^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/Mat