CR-Yamabe方程的存在性结果

IF 0.2 Q4 MATHEMATICS

Bruno Pini Mathematical Analysis Seminar Pub Date : 2013-12-23 DOI:10.6092/ISSN.2240-2829/4017

Vittorio Martino

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引用次数: 0

摘要

本文将证明CR-Yamabe方程有无穷多个变号解。问题是变分的，但相关的泛函不满足palais - small紧性条件;通过适当的群作用，我们定义了一个子空间，在该子空间上我们可以应用Ambrosetti-Rabinowitz的极大极小论证。这一结果解决了80年代Jerison-Lee对正解的分类结果留下的一个问题。

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Existence result for the CR-Yamabe equation

In this note we will prove that the CR-Yamabe equation has infinitely many changing-sign solutions. The problem is variational but the associated functional does not satisfy the Palais-Smale compactness condition; by mean of a suitable group action we will define a subspace on which we can apply the minimax argument of Ambrosetti-Rabinowitz. The result solves a question left open from the classification results of positive solutions by Jerison-Lee in the '80s.

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来源期刊

Bruno Pini Mathematical Analysis Seminar MATHEMATICS-

CiteScore

0.30

自引率

0.00%

发文量

审稿时长

15 weeks