The existence of nontrivial solutions for the critical Kirchhoff type problem in RN

In this paper, we study the problem (0.1)−a+b∫RN|∇u|2dxΔu+V(x)u=μf(u)+g(x)u2∗−1inRN,where N≥3, a, b>0. When N=3 and μ>0 is small, under suitable conditions on V, f and g, we prove (0.1) has two nontrivial solutions. When N≥4 and g(x)=1, we also obtain the existence and non-existence results.