In this paper, we investigate a class of nonlinear Kirchhoff-type equation - (a+b ₑ^₍| u|^2dx) u-f (u) = u+|u|^p-2u, x R^{N}, where a, b, c>0 are prescribed, R arises as a Lagrange multiplier and the normalized constrain ₑ^₍|u|^2dx=c^2 is satisfied in the case 1 N 3. The nonlinearity f is mass subcritical or supercritical and 2< p<2+8N or 2+8N< p<2^*. By making a series of assumptions about f, we obtain the existence or the nonexistence of ground state solutions via minimizing methods.
Yi et al. (Mon,) studied this question.