LAUSR

Abstract In the present paper, we investigate the following degenerate Kirchhoff type problem { − ( b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = | u | 2 ⁎ − 2 u in R N , u ∈ D 1 , 2 ( R N ) , where b is a positive constant, V ∈ 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.