A perturbed problem of elliptic system with critical exponent. Issue 14 (22nd September 2022)

• Record Type: Journal Article
• Authors: Li, Qi; Zheng, Binbin
• Is Part Of: Applicable analysis. Volume 101:Issue 14(2022)
• Page Start: 4982
• Page End: 4990
• Publication Date: 2022-09-22
• Subjects: Perturbation argument -- Lyapunov–Schmidt reduction method -- critical exponent; 35J47 -- 35J50; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1877681
• Languages: English
• ISSNs: 0003-6811

Abstract

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.