一类具有非局部非线性的半线性椭圆方程的Liouville型定理和Morse指标

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI:10.1063/5.0091269

Xiaowei An, Huixia He, Xianfa Song

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引用次数: 0

摘要

本文研究了一类具有非局部非线性的半线性椭圆型方程的解。利用山口定理、Hölder不等式和Sobolev嵌入定理，得到了方程的存在性结果，建立了Liouville型定理，并考虑了方程的Morse指标。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Liouville type theorem and Morse indices of a semilinear elliptic equation with nonlocal nonlinearities

In this study, we study the solution of a semilinear elliptic equation with nonlocal nonlinearities. By using the mountain pass theorem, Hölder’s inequality, and Sobolev embedding theorem, we obtain the existence result, establish the Liouville type theorem, and consider Morse indices of the equation.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.