一类半线性椭圆型方程组正解的存在性  

Existence of positive solutions for a class of semilinear elliptic systems

作　　者：郭伟香 杨燕君 张亚静[1] GUO Wei-xiang;YANG Yan-jun;ZHANG Ya-jing(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《云南民族大学学报（自然科学版）》2019年第1期46-53,共8页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(61374089;11871315)

摘　　要：主要研究一类半线性椭圆型方程组正解的存在性.利用变分法将椭圆型方程组解的问题转化为相应能量泛函的临界点问题,进一步证明了方程组能量泛函临界点的存在性.This paper mainly studies the existence of positive solutions for a class of semilinear elliptic systems. By using the variational method, the problem of solving elliptic equations is transformed into the critical point problem of the corresponding energy functional, and the existence of the critical point of the energy functional of the equations is further proved.

关 键 词：变分法 NEHARI流形 上下解方法 正解 

分 类 号：O175.29[理学—数学]