Fundamental Frequency Solutions with Prescribed Action Value to Nonlinear Schrödinger Equations

We apply the nonlinear generalized Rayleigh quotients method to develop new tools that can be used study ground states of Schrödinger equations. introduce a type variational functional, global minimizer which corresponds so-called fundamental frequency solutions with prescribed action value. find state problem and uniquely determine corresponding values mass, frequency, level. Based on this approach, we obtain results existence absence nonnegative zero mass problem.