Normalized solutions to the quasilinear Schrödinger equations with combined nonlinearities

We consider the radially symmetric positive solutions to quasilinear problem {equation*}- u-u u²+λ u=f(u),{ in} \ RN,{equation*} having prescribed mass ∫_RN|u|² =a², where a > 0 is a constant, λ appears as a Lagrange multiplier. We focus on the pure L 2 -supercritical case and combination case of L 2 -subcritical and L 2 -supercritical nonlinearities {equation*}f(u)=τ |u|q-2u+|u|ᵖ⁻²u, τ > 0,{ where}\ \ 2 < q < 2+4/N \ { and} \ p > p̄,{equation*} where p̄:=4+4/N is the L 2 -critical exponent. Our work extends and develops some recent results in the literature.