A non-existence result for low energy sign-changing solutions of the Brezis Nirenberg problem in dimensions 4, 5 and 6

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Dammak, Yessine^1,2,3 

[1] Sfax Univ, Sfax Business Sch, Sfax, Tunisia

[2] Sfax Univ, Fac Sci Sfax, Sfax, Tunisia

[3] Sfax Business Sch, BP 1081, Sfax 3018, Tunisia

关键词: Blow-up analysis;    Sign-changing solutions;    Lack of compactness;    Critical exponent;   

DOI  :  10.1016/j.jde.2017.08.020

来源: Elsevier

【 摘 要 】

We consider the Brezis Niremberg problem: (P-epsilon) {-Delta u = vertical bar u vertical bar(p-1) u + epsilon u in Omega, u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-n, n = 4, 5, 6, p + 1 = 2n/n-2 is the critical Sobolev exponent and epsilon is a positive parameter. The main result of the paper generalizes the result of A. Iacopetti and F. Pacella [10]. Precisely we show that there are no low energy sign-changing solutions u(epsilon) with max u(epsilon) / min u(epsilon) -> 0 or -infinity as epsilon goes to zero. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free