On ground states for the Kirchhoff-type problem with a general critical nonlinearity

In this paper, we consider the following Kirchhoff-type problem{−(a+b∫R3|∇u|2)Δu=f(u),inR3,u∈H1(R3),u>0,inR3, where a,b>0a,b>0 are constants, and f   has a critical growth. The aim of this paper is to study the existence of ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth, without the assumption of the monotonicity of the function t→f(t)t3. Moreover, we will show that the mountain pass value gives the least energy level and also obtain a mountain pass solution.