A perturbed problem of elliptic system with critical exponent. Issue 14 (22nd September 2022) - Li, Qi; Zheng, Binbin
ABSTRACT: This paper deals with the following perturbed problem with critical exponent (1) − Δ u = u 2 ∗ − 1 + α 2 ∗ u α − 1 v β + ϵ K ( x ) u p, x ∈ R N, − Δ v = v 2 ∗ − 1 + β 2 ∗ u α v β − 1 + ϵ Q ( x ) v q, x ∈ R N, u > 0, v > 0, x ∈ R N, where 1 ≤ p, q < 2 ∗ − 1, α + β = 2 ∗ := 2 N N − 2, α, β ≥ 2, N = 3, 4 and ε is a parameter. Using a perturbation argument and Lyapunov–Schmidt reduction method, we obtain the existence of positive solutions to problem (1) and the asymptotic property of the solutions.