QUASILINEAR SCHRODINGER EQUATIONS: GROUND STATE AND INFINITELY MANY NORMALIZED SOLUTIONS

We study the normalized solutions for the following quasilinear Schrodinger equations: -Delta u - u Delta u(2) + lambda u = vertical bar u vertical bar(p-2)u in R-N, with prescribed mass integral(RN) u(2) = a(2). We first consider the mass-supercritical case p > 4 + 4/N, which has not been studied before. By using a perturbation method, we succeed to prove the existence of ground state normalized solutions, and by applying the index theory, we obtain the existence of infinitely many normalized solutions. We also obtain new existence results for the mass-critical case p = 4 + N/4 and remark on a concentration behavior for ground state solutions.