  By introducing and solving two correlative constrained variational problems
as well as spectrum analysis, an approach to fix soliton frequency from the
prescribed mass for nonlinear Schr\"odinger equations is found, and an open
problem in normalized solutions is answered. Then existence and orbital
stability of big solitons depending on frequencies for nonlinear Schr\"odinger
equation with competitive power nonlinearity is proved for the first time. In
addition multi-solitons of the equation with different speeds are constructed
by stable big solitons.
