平均场方程的平凡解和非平凡解的对称性

IF 0.7 4区数学 Q2 MATHEMATICS

Annales Polonici Mathematici Pub Date : 2020-01-01 DOI:10.4064/ap191126-30-6

Jiaming Jin, Chuanxi Zhu

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引用次数: 0

摘要

我们考虑s上的平均场方程α 2∆gu+ e u−1 = 0，并证明在某些技术条件下，当1/3≤α < 1时，u必须一直为零。特别地，这是当u(x) = - u(- x)并且u是奇对称平面的情况。在u(x) = - u(- x)且1/3≤α < 1和u(x) = u(- x)且1/4≤α < 1的情况下，详细分析了非平凡解的附加对称性。

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Trivial solution and symmetries of nontrivial solutions to a mean field equation

We consider the mean field equation α 2 ∆gu+ e u − 1 = 0 on S. We show that under some technical conditions, u has to be constantly zero for 1/3 ≤ α < 1. In particular, this is the case if u(x) = −u(−x) and u is odd symmetric about a plane. In the cases u(x) = −u(−x) with 1/3 ≤ α < 1 and u(x) = u(−x) with 1/4 ≤ α < 1, we analyze the additional symmetries of the nontrivial solution in detail.

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来源期刊

Annales Polonici Mathematici 数学-数学

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： Annales Polonici Mathematici is a continuation of Annales de la Société Polonaise de Mathématique (vols. I–XXV) founded in 1921 by Stanisław Zaremba. The journal publishes papers in Mathematical Analysis and Geometry. Each volume appears in three issues.