A perturbed Kirchhoff problem with critical exponent. Issue 11 (18th August 2021) - Aissaoui, Narimane
ABSTRACT: 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.