Existence of positive ground state solutions for a critical Kirchhoff type problem with sign-changing potential

In this work, we are interested in studying the following Kirchhoff type problem {- (a+b integral(Omega) vertical bar del u vertical bar(2)dx) Delta u = f(x)vertical bar u vertical bar(2*-2)u+lambda g(x)vertical bar u vertical bar(q-1)u, x is an element of Omega, u = 0, x is an element of partial derivative Omega, where Omega subset of R-N(N >= 3) is a smooth bounded domain, 2* = 2N/N-2 is the critical Sobolev exponent, 0 < q < 1, lambda > 0, and f is an element of L-infinity(ohm) with the set {x is an element of Omega : f(x) > 0} of positive measures, and g is an element of L-infinity(Omega) with g(x) >= 0, g not equivalent to 0. By the Nehari method and variational method, the existence of positive ground state solutions is obtained. (C) 2018 Elsevier Ltd. All rights reserved.