奇异椭圆方程Robin问题多重正解的存在性  

Existence of Multiple Positive Solutions for the Robin Problem of Singular Elliptic Equations

作　　者：吴德科 索洪敏 WU Deke;SUO Hongmin(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《应用数学》2022年第1期53-65,共13页Mathematica Applicata

基　　金：国家自然科学基金(11861021);国家自然科学基金(11661021)。

摘　　要：本文研究奇异椭圆方程Robin边值问题.首先运用Nehari流形方法解决带奇异项问题所对应泛函在零点处不可微的难点,其次应用Ekeland变分原理得到该问题对应泛函存在的临界点,最后通过极大值原理得到两个正解的存在性.We consider the following the Robin boundary problem of singular elliptic equations.Firstly, Nehari manifold method is used to solve the difficulty that the functional with singular term cannot be differentiable at zero. Secondly, the critical points of the functional existence corresponding to this problem are obtained by using the Ekeland variational principle. Finally, the existence of two positive solutions is obtained by using the maximum principle.

关 键 词：Robin边值 NEHARI流形 奇异项 

分 类 号：O175.2[理学—数学]