平面上椭圆型正弦-戈登方程有限Morse指数解的分类

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-08-02 DOI:10.4171/rmi/1296

Yong Liu, Juncheng Wei

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引用次数: 1

摘要

椭圆型正弦-戈登方程是一类具有特殊双阱势的半线性椭圆方程。它有一系列显式的多端解。我们证明了所有有限摩尔斯指数解都属于这个族。我们还将证明这些解是非退化的，即相应的线性化算子没有非平凡有界核。最后，我们证明了2n端解的摩尔斯指数等于n(n−1)/2。

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Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane

The elliptic sine-Gordon equation is a semilinear elliptic equation with a special double well potential. It has a family of explicit multiple-end solutions. We show that all the finite Morse index solutions belong to this family. It will also be proved that these solutions are nondegenerate, in the sense that the corresponding linearized operators have no nontrivial bounded kernel. Finally, we prove that the Morse index of 2n-end solutions is equal to n(n−1)/2.

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来源期刊

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.