Ground states for Kirchhoff equations without compact condition

In this paper, we consider the following nonlinear problem of Kirchhoff-type with general nonlinearities:equation(0.1){−(a+b∫R3|∇u|2)Δu+V(x)u=f(u),inR3,u>0,inR3,u∈H1(R3), where a>0a>0, b≥0b≥0 are two constants and V:R3→RV:R3→R is a potential function. Under certain assumptions on V and f, we prove that (0.1) has a positive ground state solution by using variational methods. The character of this work is that we don't assume the classical Ambrosetti–Rabinowitz condition on f   which is essential to obtain the boundedness of a (PS)c(PS)c sequence.