河南师范大学学报(自然科学版)

2021, v.49;No.221(06) 70-76

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一类非局部奇异椭圆方程组多解的存在性
Multiple solutions for a class of nonlocal singular elliptic system

陈林;汤楠;
Chen Lin;Tang Nan;College of Mathematics and Statistic, Yili Normal University;

摘要(Abstract):

研究一类非局部奇异椭圆方程组多解的存在性.首先,通过对方程组两边积分得到方程组弱解的定义;其次,构造Nehari流形以缩小寻找解的范围;最后,引入纤维环映射并运用变分法证明了此问题至少存在两个正解.
In this paper, we study the existence and multiplicity to a class to nonlocal singular elliptic system. Firstly, the definition of weak solution to the equations is obtained by integrating both sides of the equations. Secondly, Nehari manifold is constructed to narrow the existence range of solutions. Finally, we prove that the problem has at least two positive solutions by introducing fibering map and using variational methods.

关键词(KeyWords): 椭圆方程组;Nehari流形;纤维环映射;变分法
elliptic system;Nehari manifold;fibering map;variational method

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11461075);; 伊犁师范大学博士科研启动基金项目(2017YSBS08);; 新疆高校科研计划重点资助项目(XJEDU2016I043)

作者(Author): 陈林;汤楠;
Chen Lin;Tang Nan;College of Mathematics and Statistic, Yili Normal University;

Email:

DOI: 10.16366/j.cnki.1000-2367.2021.06.010

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