Normalized solutions to a class of Kirchhoff equation with general nonlinearity: mass subcritical or supercritical

In this paper, we investigate a class of nonlinear Kirchhoff-type equation - (a+b∫ _RN|∇ u|²dx )Δ u-f(u)= λ u+|u|ᵖ⁻²u,x∈ RN, where $a,b,c>0$ are prescribed, λ ∈ R arises as a Lagrange multiplier and the normalized constrain ∫ _RN|u|²dx=c² is satisfied in the case 1≤ N≤ 3. The nonlinearity f is mass subcritical or supercritical and 2< p<2+8/N or 2+8/N< p<2*. By making a series of assumptions about f, we obtain the existence or the nonexistence of ground state solutions via minimizing methods.