带有两个奇异项的p(x)-Laplace方程解的存在性多解性研究  

Existence and Multiple Solutions of p(x)Laplace Equation with Two Singular Terms

作　　者：胡新存 陈海波[1] Hu Xincun;Chen Haibo(School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]中南大学数学与统计学院,长沙410075

出　　处：《数学理论与应用》2023年第2期68-81,共14页Mathematical Theory and Applications

基　　金：the National Natural Science Foundation of China(No.12071486)。

摘　　要：本文研究带有两个奇点的P(x)-Laplace算子{−∆p(x)u+V(x)|u|^(p(x)−2u)=µ|u|s(x)−2u/|x|^(s(x))+λh(x)u^(−γ(x))的正解的存在性和多解性.由于上述方程中奇异项u(-γ(x))和|x|(-s(x))的出现,使得其正解存在性的证明更加困难.我们通过使用Nehari流形的分解和一些精确的估计,证明上述方程至少有两个正解.In this paper,we study the existence and multiplicity of positive solutions for the following double singular problem with p(x)Laplace operator{−∆p(x)u+V(x)|u|^(p(x)−2u)=µ|u|s(x)−2u/|x|^(s(x))+λh(x)u^(−γ(x))inΩ,u=0 on∂Ω.Due to the presence of singular term u^(−γ(x))and singular potential|x|^(−s(x))in the equation,it is more difficult to deal with the existence of positive solutions.By using the decomposition of Nehari manifold and some refined estimates,we show that there admits at least two positive solutions for the double singular problem.

关 键 词：NEHARI流形 p(x)-Laplace算子 奇数项 变分法 

分 类 号：O175[理学—数学]