加权Schrödinger-Hartree-Maxwell型方程组非负解的刘维尔定理  

Liouville Theorems for Nonnegative Solutions to Weighted Schrödinger-Hartree-Maxwell Type System

作　　者：李云亭 刘亚琼 肖迎迎 Li Yunting;Liu Yaqiong;Xiao Yingying(School of Mathematics and Computer Science,Jiangxi Science and Technology Normal University,Nanchang 330038,Jiangxi,P.R.China)

机构地区：[1]江西科技师范大学数学与计算机科学学院,江西南昌330038

出　　处：《江西科技师范大学学报》2022年第6期95-101,共7页Journal of Jiangxi Science & Technology Normal University

基　　金：江西省教育厅科学技术重点项目(GJJ211101);江西科技师范大学研究生创新专项资金项目(YC2022-X09)。

摘　　要：本文主要考虑加权Schrödinger-Hartree-Maxwell型方程组在次临界情况下非负解的刘维尔定理(即非负非平凡解的不存在性)。证明过程中主要运用反证法和放缩球体法,以及通过微分方程组与积分方程组之间的等价性,得到解的下界估计与积分方程组解的可积性相矛盾,随后证得加权Schrödinger-Hartree-Maxwell型方程组非平凡非负解的不存在性。This paper mainly concerned with the Liouville theorems(i.e., non-existence of nontrivial nonnegative solutions) for nonnegative solutions to weighted Schrödinger-Hartree-Maxwell type system in the subcritical cases. In the process of proof, the method of contradiction and scaling spheres are mainly used, and through the equivalence between differential system and integral system, it is found that the lower bound estimation of solutions conflicts with the integrability of solutions of integral equations, and then the non-existence of nontrivial nonnegative solutions of weighted Schrödinger-Hartree-Maxwell type system was proved.

关 键 词：加权Schrödinger-Hartree-Maxwell型方程组 次临界 非负解 放缩球体法 

分 类 号：O175.2[理学—数学]