A perturbed Kirchhoff problem with critical exponent. Issue 11 (18th August 2021)

• Record Type: Journal Article
• Authors: Aissaoui, Narimane; Li, Qi; Zheng, Binbin
• Is Part Of: Applicable analysis. Volume 100:Issue 11(2021)
• Page Start: 2368
• Page End: 2385
• Publication Date: 2021-08-18
• Subjects: S. Leonardi; Kirchhoff problem -- perturbed argument -- finite-dimensional reduction; 35A01 -- 35J60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1687884
• Languages: English
• ISSNs: 0003-6811

Abstract

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.