Positive solutions for Kirchhoff-type equations with critical exponent in RNRN

In this paper, we study the following nonlinear Kirchhoff-type equationequation(0.1){−(a+b∫RN|∇u|2dx)△u=|u|2⁎−2u+μh(x),x∈RNu∈D1,2(RN), where a≥0a≥0, b>0b>0, N≥3N≥3, 2⁎=2NN−2, μ≥0μ≥0 and h∈L2⁎2⁎−1(RN)\{0} is nonnegative. By using the variational method, we obtain the existence of positive solutions for Eq. (0.1), under some assumptions on a, b, μ.