Positive solutions for a critical p-Laplacian problem with a Kirchhoff term

In this article, the following p-Laplacian problem with Kirchhoff term and critical exponent is studied {-(a + b integral(N)(R) vertical bar del u vertical bar(p)dx)(,) Delta(p)u = up*(-1) + mu h(x), x is an element of R-N, u is an element of D-1,D-p(R-N), where alpha, mu >= 0, b > 0, 1 < p < N, p* = Np/N-p, Delta(p)u = div (vertical bar del u vertical bar(p-2)del), and h is an element of Lp*/p*-1(R-N) is nonzero and nonnegative. When mu, = 0, with the help of the recent result of B. Sciunzi(Adv. Math. 291(2016) 12-23), infinitely many positive solutions are obtained by some analysis techniques. While mu. > 0, by the variational method, some results about positive solutions are obtained. (C) 2018 Elsevier Ltd. All rights reserved.