一类具变号权函数的椭圆型p-Laplace方程弱解的多重性  

Multiplicity of Weak Solutions for a Class of p-Laplacian Elliptic Equations with Sign-Changing Weight Function

作　　者：刘鲜 高文杰[1] 韩玉柱[1] LIU Xian;GAO Wenjie;HAN Yuzhu(Collegeof Mathematics,JilinUniversity,Changchun 130012,China)

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2019年第1期1-8,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11401252);吉林省科技厅青年基金(批准号:20160520103JH)

摘　　要：考虑一类具变号权函数的椭圆型p-Laplace方程弱解的多重性,借助Nehari流形和对数型Sobolev不等式,证明了该问题至少存在两个非平凡弱解.We considered the multiplicity of weak solutions for a class of p-Laplacian elliptic equations with sign-changi ng weight function.By means of Nehari’s manifold and logarithmic Sobolev inequali ty,we proved that there were at least two nontrivial weak solutions to the problem.

关 键 词：变号权函数 多重性 NEHARI流形 

分 类 号：O175.8[理学—数学]