R^(N)空间中具有临界增长的线性耦合双调和系统的正解  

Positive Solutions for a Linearly Coupled Biharmonic System Involving Critical Growth in R^(N)

作　　者：许丽萍[1] XU Liping(Department of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471000,China)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471000

出　　处：《应用数学》2023年第2期304-318,共15页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(10671182)。

摘　　要：本文研究R^(N)空间中一类具有线性耦合的双调和系统.当非线性项分别具有次临界和临界增长的条件时,利用Nehari流形方法,获得该系统正基态解存在性的多个结果,同时借助Pohozaev等式还得到该系统正解不存在的结果.In this paper,we deal with a class of linearly coupled biharmonic system.Under the assumptions on the nonlinear terms being subcritical or critical,we establish the existence of positive ground state solutions for the system via Nehari manifold method.As its supplementary results,we also obtain the nonexistence of positive solutions.

关 键 词：线性耦合双调和系统 基态解 Nehari流形方法 正解的不存在性 

分 类 号：O175.14[理学—数学]