一类带临界指数的半线性椭圆系统第二个正解的存在性  

Existence of the Second Positive Solution for A Class of Semilinear Elliptic System with Critical Exponent

作　　者：廖家锋 周秀 LIAO Jia-feng;ZHOU Xiu(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2023年第2期131-140,共10页Journal of China West Normal University(Natural Sciences)

基　　金：四川省自然科学基金项目(2022NSFSC1816);西华师范大学基本科研项目(18B015)。

摘　　要：本文研究了一类带临界指数的半线性椭圆系统,克服了临界指数项产生的困难。首先,给出Nehari流形的定义,且将Nehari流形分为三部分;其次,证明系统对应的能量泛函满足(PS)_(c)条件,从而获得泛函的紧性条件;最后,在Nehari流形上利用变分法证明该系统第二个正解的存在。该结果完善了带临界指数的半线性椭圆系统第二个正解结果,并给出这类系统问题新的可解性条件。This paper talks about a class of semilinear elliptic system with critical exponent and solves the difficulty brought by critical exponent.Firstly,the definition of Nehari manifold is given,which is then divided into three parts.Secondly,the compactness condition is obtained by proving that the corresponding energy function satisfies the(PS)_(c)condition.Finally,the existence of second positive solution for this system is proved by employing the variational method on Nehari manifold.The result has improved the existence of the second positive solution for semilinear elliptic system with critical exponent.Moreover,a new solvable condition for this system is presented.

关 键 词：半线性椭圆系统 临界指数 正解 Nehari流形方法 变分法 

分 类 号：O177.91[理学—数学]