Global asymptotic behavior of solutions to quasilinear Schrödinger equations

Abstract

We are concerned with the existence and blowup of solutions for a class of quasilinear Schrödinger equations. In particular, we examine the combined effect of local type nonlinearity and Hartree type ones, and depending upon different parameter regimes, we find the dominant roles exhibited by these nonlinear effects. We also consider the asymptotic behavior for the global solution and lower bound for the blowup rate of the blowup solution by using pseudo-conformal conservation laws.