Normalized solutions to the quasilinear Schrödinger equations with combined nonlinearities

Abstract We consider the radially symmetric positive solutions to quasilinear problem equation*- u-u u^2+ u=f (u), in \ R^N, equation* having prescribed mass ₑ^₍|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) = |u|^q-2u+|u|^p-2u, 0, where\ \ 2 q 2+4N \ and \ p p, equation* where p: =4+4N is the L 2 -critical exponent. Our work extends and develops some recent results in the literature.