Characterization of ground states for an M-coupled system in a bounded domain with critical exponent
Characterization of ground states for an M-coupled system in a bounded domain with critical exponent
复制标题
具有临界指数的有界域中 M 耦合系统的基态表征
DOI：
10.1002/mma.6429
复制
发表时间：
2020
影响因子：
2.9
通讯作者：
Yang Jing
中科院分区：
文献类型：
--
作者：
He Qihan;Yang Jing
本文主要研究有界区域上的M-耦合系统−Δui+λiui=∑j= 1 M κ ij 2 qij 2 *| uj| PIJ| UI| qij−2ui，y∈Ω，ui∈ H 01（Ω），i= 1，2，.，M，其中有界且在{λi}和{κij}的某些假设下，用纯变分方法证明了上述系统基态的存在性.进一步讨论了在λi（i= 1，2，.，M）附近的附加条件下基态的特征，并研究了基态的个数，包括正基态和半平凡基态.
In this paper, we focus on the following M‐coupled system in a bounded domain −Δui+λiui=∑j=1Mκij2qij2*|uj|pij|ui|qij−2ui,y∈Ω,ui∈H01(Ω),i=1,2,…,M, whereis bounded andBy purely variational methods, the existence of ground states to the above system under some assumptions on {λi} and {κij} is proved. Furthermore, we discuss the characterization of the ground states under additional conditions aboutλi(i=1,2,…,M), and we study the number of the ground states, containing the positive ground states and the semitrivial ground states.