Bounded state solution of degenerate Kirchhoff type problem with a critical exponent

In the present paper, we investigate the following degenerate Kirchhoff type problem {-(b integral(RN) vertical bar del u vertical bar(2)dx)Delta u+V(x)u=vertical bar u vertical bar(2*-2)u in R-N, u is an element of D-1,D-2 (R-N), where b is a positive constant, V is an element of L-N/2 (R-N) is a given nonnegative function and 2* is the critical exponent. Quite a few papers have been published about the degenerate Kirchhoff type problem with a critical exponent; moreover, this degenerate problem in R-N (N >= 5) has never been considered so far. We obtain some sufficient conditions on the existence of bounded state solution for this degenerate problem. As to the cases where N >= 5, it is the first time to consider the degenerate problem. (C) 2019 Elsevier Inc. All rights reserved.