A nonexistence result for sign-changing solutions of the Brezis-Nirenberg problem in low dimensions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Iacopetti, Alessandro¹  Pacella, Filomena² 

[1] Univ Roma Tre, Dipartimento Matemat & Fis, I-00146 Rome, Italy

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

关键词: Semilinear elliptic equations;    Critical exponent;    Sign-changing solutions;    Asymptotic behavior;   

DOI  :  10.1016/j.jde.2015.01.030

来源: Elsevier

【 摘 要 】

We consider the Brezis-Nirenberg problem: [GRAPHICS] where Omega is a smooth bounded domain in R-N, N >= 3,2* = 2N/N-2 is the critical Sobolev exponent and lambda > 0 is a positive parameter. The main result of the paper shows that if N = 4, 5, 6 and lambda is close to zero, there are no sign-changing solutions of the form u(lambda) = PU delta 1,xi, PU delta 2,xi,+ omega(lambda), where PU delta is the projection on H-0(1)(Omega) of the regular positive solution of the critical problem in RN, centered at a point xi epsilon Omega and w(lambda) is a remainder term. Some additional results on norm estimates of w(lambda), and about the concentrations speeds of tower of bubbles in higher dimensions are also presented. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free