A perturbed Kirchhoff problem with critical exponent.

In this paper, we consider a class of Kirchhoff problems as follows (1) − a + b ∫ R N | ∇ u | 2 Δ u = (1 + ε K (x)) u 2 ∗ − 1 , u > 0 i n R N , where a, b>0 are given constants, ϵ is a small parameter and 2 ∗ = 2 N / (N − 2) , N ≥ 3. We first prove the nondegeneracy of positive solutions to Equation (1) when ε = 0. Then, as an application, using a perturbed argument and finite-dimensional reduction method, we prove the existence of positive solutions of Equation (1) for ϵ small. [ABSTRACT FROM AUTHOR]