NORMALIZED SOLUTIONS TO THE QUASILINEAR SCHRODINGER EQUATIONS WITH COMBINED NONLINEARITIES

We consider the radially symmetric positive solutions to quasilinear problem -Delta u - u Delta u(2) + lambda u = f(u), in R-N, having prescribed mass integral(N)(R) |u|(2) = a(2), where a > 0 is a constant, lambda 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 f(u) = tau|u|(q-2)u + |u|(p-2)u, tau > 0, where 2 < q < 2 + 4/N and p > p, where p := 4 + 4/N is the L-2-critical exponent. Our work extends and develops some recent results in the literature.