Complex group actions on the sphere and sign changing solutions for the CR-Yamabe equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Maalaoui, Ali¹  Martino, Vittorio²  Tralli, Giulio² 

[1] Amer Univ Ras Al Khaimah, Dept Math & Nat Sci, Ras Al Khaymah, U Arab Emirates

[2] Univ Bologna, Dipartimento Matemat, I-40127 Bologna, Italy

关键词: Sub-elliptic PDE;    Critical points theory;    Minimax method;   

DOI  :  10.1016/j.jmaa.2015.05.057

来源: Elsevier

【 摘 要 】

In this paper we prove that the CR-Yamabe equation on the sphere has infinitely many sign changing solutions. The problem is variational but the related functional does not satisfy the Palais Smale condition, therefore the standard topological methods fail to apply directly. To overcome this lack of compactness, we will exploit different group actions on the sphere in order to find suitable closed subspaces, on which the restricted functional is Palais Smale: this will allow us to use the minimax argument of Ambrosetti-Rabinowitz to find critical points. By a classification of the positive solutions and by considerations on the energy blow-up, we will get the desired result. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free