Classification of solutions to the critical order elliptic system with general nonlinearity  

作　　者：Yuxia Guo Shaolong Peng 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2025年第4期807-838,共32页中国科学(数学英文版)

基　　金：supported by National Key R&D Program(Grant No.2023YFA1010002);National Natural Science Foundation of China(Grant Nos.12031015 and 12271283)。

摘　　要：Consider the following elliptic system:{(−∆)u=f(u,v),(−∆)v=g(u,v),(0.1)where f and g are continuous functions and satisfy the finite total curvature conditions.Recently,Guo and Liu(2008)derived Liouville-type results for the positive solution of the semilinear elliptic system(0.1)in the whole space R^(N)(N≥3).However,the case N=2 is different and difficult because u and v may change signs.Using the method of moving spheres in the integral form combined with integral inequalities,we give a complete classification of the classical solutions to the above system in R2.This seems the first result for the classification of solutions(u,v)(here u and v are not required to be positive solutions)to the critical order system(0.1)in the two-dimensional case.

关 键 词：classification of solutions semilinear elliptic system method of moving spheres critical order 

分 类 号：O175.25[理学—数学]